Angela and Zooey want to open a restaurant serving fish and beef dishes but have limited funds. They can make 60 meals total and want to maximize profit. A linear programming model shows they should make 40 fish meals at $12 each and 20 beef meals at $16 each for $800 profit. Increasing the fish price to $16 would raise profit to $960 without reducing customers. Spending $30 on advertising that increases sales by 10 meals would gain $80 in profit. Reducing labor by 5 hours could lower profits, so more reliable staff should be hired. Raising the fish price to $14 would gain $80 in profit.
The document discusses how changes in income, prices of substitutes and complements, taxes, and technology would impact the demand and supply of goods X and Y. It also provides an example equilibrium calculation for a good with given demand and supply functions and determines the new equilibrium price and quantity when a $6 excise tax is levied. The tax generates $6 in total tax revenue based on 1 unit sold at the new equilibrium.
This document discusses monopolistic competition and oligopoly. It begins by outlining the topics to be discussed, which include monopolistic competition, oligopoly, price competition, and the prisoner's dilemma as it relates to oligopolistic pricing. It then provides characteristics and examples of monopolistic competition, including differentiated products with free entry and exit. It analyzes a monopolistically competitive firm's behavior and profits in the short and long run. It also discusses oligopoly characteristics like having a small number of firms and barriers to entry. It provides examples of oligopolistic industries and analyzes oligopoly models including Cournot, Bertrand, and Stackelberg. It concludes with a pricing problem scenario involving Procter & Gamble, K
This document provides an overview and summary of a textbook on basic microeconomics. It discusses the origins and licensing of the textbook, which was originally authored by Professor R. Larry Reynolds and is now distributed by Textbook Equity under a Creative Commons license. The textbook covers topics such as the nature of economics as a social science, the problem of provisioning resources, ways of knowing including the scientific method, individuals and communities, criteria for evaluation, and different economic systems. It is made freely available in PDF and paperback formats.
This document discusses linear programming applications in marketing, manufacturing, and other areas. It provides examples to demonstrate how to model and solve linear programming problems involving media mix optimization, production scheduling, inventory management, and other scenarios. Specifically, it presents sample problems and solutions involving marketing mix optimization for a gambling club, sampling costs for a market research firm, production planning for a tie manufacturer, and multi-period production scheduling for an electric motor company. The chapter aims to illustrate how to apply linear programming to optimize objectives subject to constraints across various business applications.
The document provides information about an inventory class including:
- Topics covered inventories, inventory valuation, biological assets, gross profit, and retail inventory method.
- Formulas and calculations for inventory costing methods like FIFO, weighted average, and retail inventory method are presented.
- An example problem demonstrates estimating ending inventory cost using the gross profit method.
Using binary integer linear programming to deal with yes no decisions.KattareeyaPrompreing
Using binary integer linear programming to deal with yes no decisions.
By Kattareeya Prompreing - Ph.D. student in Business and Management,College Business, Southren Taiwan University of Science and Technology
The document discusses how changes in income, prices of substitutes and complements, taxes, and technology would impact the demand and supply of goods X and Y. It also provides an example equilibrium calculation for a good with given demand and supply functions and determines the new equilibrium price and quantity when a $6 excise tax is levied. The tax generates $6 in total tax revenue based on 1 unit sold at the new equilibrium.
This document discusses monopolistic competition and oligopoly. It begins by outlining the topics to be discussed, which include monopolistic competition, oligopoly, price competition, and the prisoner's dilemma as it relates to oligopolistic pricing. It then provides characteristics and examples of monopolistic competition, including differentiated products with free entry and exit. It analyzes a monopolistically competitive firm's behavior and profits in the short and long run. It also discusses oligopoly characteristics like having a small number of firms and barriers to entry. It provides examples of oligopolistic industries and analyzes oligopoly models including Cournot, Bertrand, and Stackelberg. It concludes with a pricing problem scenario involving Procter & Gamble, K
This document provides an overview and summary of a textbook on basic microeconomics. It discusses the origins and licensing of the textbook, which was originally authored by Professor R. Larry Reynolds and is now distributed by Textbook Equity under a Creative Commons license. The textbook covers topics such as the nature of economics as a social science, the problem of provisioning resources, ways of knowing including the scientific method, individuals and communities, criteria for evaluation, and different economic systems. It is made freely available in PDF and paperback formats.
This document discusses linear programming applications in marketing, manufacturing, and other areas. It provides examples to demonstrate how to model and solve linear programming problems involving media mix optimization, production scheduling, inventory management, and other scenarios. Specifically, it presents sample problems and solutions involving marketing mix optimization for a gambling club, sampling costs for a market research firm, production planning for a tie manufacturer, and multi-period production scheduling for an electric motor company. The chapter aims to illustrate how to apply linear programming to optimize objectives subject to constraints across various business applications.
The document provides information about an inventory class including:
- Topics covered inventories, inventory valuation, biological assets, gross profit, and retail inventory method.
- Formulas and calculations for inventory costing methods like FIFO, weighted average, and retail inventory method are presented.
- An example problem demonstrates estimating ending inventory cost using the gross profit method.
Using binary integer linear programming to deal with yes no decisions.KattareeyaPrompreing
Using binary integer linear programming to deal with yes no decisions.
By Kattareeya Prompreing - Ph.D. student in Business and Management,College Business, Southren Taiwan University of Science and Technology
PACK-iTS case Analyse and recommendation. short and brief powerpoint presentation .2 slide ppt . discussed inside are the problem , inference and recommendations.
This document contains a chapter summary for a quantitative analysis textbook. It includes 54 multiple choice questions covering topics related to linear programming models, including graphical and computer solution methods. Key topics assessed include formulating linear programming problems, the requirements and assumptions of linear programs, graphical solutions, special cases like infeasibility and redundancy, and sensitivity analysis.
1. The document discusses quantity discount models, including calculating optimal order quantities (Q*) based on setup, holding, and product costs to determine the lowest total cost.
2. It provides examples of applying these models to determine optimal order quantities for various products given annual demand, costs, and discount price structures.
3. The optimal order quantity is the one that results in the lowest total annual cost based on comparing total costs calculated for different possible order sizes.
This document describes a linear programming problem (LPP) to minimize cost. The problem involves determining the optimal amounts of two fertilizer brands, SuperGro and CropQuick, to purchase to minimize total cost while meeting nitrogen and phosphate requirements. The LPP constructs decision variables for amounts of each brand, an objective function to minimize total cost, and constraints on nitrogen and phosphate levels. The optimal solution is to purchase 8 bags of CropQuick for a minimum total cost of 24.
This document presents a case study on supply chain management for Kar Foods. It analyzes the optimal order size for supermarkets with monthly demand of 10,000kg at different unit costs and fixed order costs. With a discount scheme, Kar Foods' profits are 60% higher at an order size of 27,500kg. However, with increased fixed costs, the discount scheme results in worse performance due to higher costs. The document recommends Kar Foods examine their discount rules and consider canceling discounts if needed. It also provides suggestions for Kar Foods such as cooperating with retailers, targeting smaller supermarkets, reducing discounts, and considering minimum order quantities.
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The document discusses sales forecasting techniques for Harmon Foods' breakfast cereal product Treat. It describes wide variability in past sales forecasts, ranging from 50-200% of actual sales. Various factors that influence demand are examined, including seasonality, promotions, and competitor strategies. The case study develops a regression model to forecast sales based on time trends, seasonality, consumer packs, and dealer allowances. Recommendations focus on timing promotions during high seasonal periods and emphasizing more effective dealer allowances over consumer packs.
Managerial Economics - The Organization of the FirmCasey Ordoña
Overview
I. Methods of Procuring Inputs
• Spot Exchange
• Contracts
• Vertical Integration
II. Transaction Costs
• Specialized Investments
• Types of Specialized Investments
Site Specificity
Physical-Asset Specificity
Dedicated Assets
Human Capital
• Implication of Specialized Investment
The document discusses markets for various goods and classifies them as perfectly competitive, monopolistically competitive, or monopolistic. It then analyzes the characteristics of firms in these different market structures and how they determine profit maximizing price and output. The document also provides examples of how individual firms might behave in these market contexts.
Macro Economics_Chapter 7_Consumers,Producers and Efficiency Marketdjalex035
This chapter discusses consumer surplus, producer surplus, and market efficiency. It defines consumer surplus as the difference between what consumers are willing to pay and what they actually pay. Producer surplus is defined as the difference between what producers are paid and their costs. The market equilibrium maximizes the total surplus, which is the sum of consumer surplus and producer surplus. This allocation of resources through supply and demand is efficient because it maximizes the total benefits to both consumers and producers.
The document contains a chapter about project management tools PERT and CPM from a quantitative analysis textbook. It includes 58 multiple choice questions about key concepts related to PERT and CPM, such as their origins and uses, time estimates, critical paths, variances, and probability calculations. The questions test understanding of network diagrams, activity dependencies, slack times, and using PERT and CPM to schedule and manage complex projects.
This document contains 50 multiple choice questions about management science concepts from Chapter 1 of the textbook "Introduction to Management Science, 10e". The questions cover topics like the management science approach, modeling techniques, variables, parameters, data, models, break-even analysis, decision support systems, and linear programming. For each question, the answer, difficulty level, page reference, and keywords are provided.
TruEarth Healthy Foods is considering launching a new line of whole grain pizzas. The document analyzes market research data to determine the potential sales volume of the new product line. It considers customer penetration rates, repeat purchase rates, and sales at different price points. Based on the analysis, the document recommends TruEarth launch the product line, estimating sales of $12.16 million assuming an 11% customer penetration rate and the ability to price between $11.38 to $12.38. Key learnings highlighted are understanding market research assumptions, analyzing data to decide on new products, and recognizing limitations of decisions based on available data.
This document provides an overview of integer programming, goal programming, and nonlinear programming. It begins with learning objectives and an outline of topics to be covered, which include integer programming, modeling with binary variables, goal programming, and nonlinear programming. Several examples are provided to illustrate integer programming problems and how they can be formulated and solved. Mixed-integer and binary variable modeling are explained. Goal programming and how it differs from linear programming in addressing multiple objectives is introduced.
Ann Banks is tasked with launching a new Italian sausage brand for Saxonville Sausage Company to meet profit objectives. She conducts market research through focus groups which reveal customers see Italian sausage as a quick meal solution. Two potential positioning concepts are identified: "Family Connection" and "Clever Cooking". Additional quantitative research shows "Clever Cooking" has higher purchase intent. Banks decides to position the new brand as "Saxonville Italian Sausage" using the "Clever Cooking" territory to appeal to time-strapped mothers. The brand will leverage Saxonville's reputation for quality and emphasize fresh, easy-to-cook attributes.
The document discusses operations research and linear programming. It defines operations research as a scientific approach to determine optimal solutions to decision problems with limited resources. Linear programming problems have decision variables, an objective function to maximize or minimize, and constraints. An optimal solution is a feasible solution that gives the most favorable objective function value. Graphical methods can find the optimal solution by determining the feasible region and optimal point.
This document provides an overview of the Business Finance course for Grade 12 students in the senior high school Academic Track. The course covers fundamental principles of financial management, financial statement analysis, financial planning tools and concepts, sources and uses of funds, basic long-term financial concepts, and an introduction to investments and personal finance. The course is designed to equip learners with skills in financial analysis, planning, and decision-making to help achieve organizational goals. It includes 80 hours of instruction organized into various content areas, with associated learning competencies and performance standards.
The document examines BP's "Beyond Petroleum" branding campaign and response to the 2010 Gulf oil spill from a marketing perspective. It finds that while the branding campaign was initially successful, the spill revealed inconsistencies between BP's brand promise of sustainability and its operations. The summary analyzes BP's crisis response, including its use of social media, finding that while the response was slow at first, BP's later aggressive social media efforts helped restore its damaged brand.
This document provides an overview of Universal Robina Corporation (URC), a major food and beverage company in the Philippines. It discusses URC's history since 1954, current business segments, leadership, goals, and competitive landscape. URC began as a corn milling plant and has since diversified into snacks, beverages, and other food categories. It aims to be the leading brand in the ASEAN region through world-class products and an efficient organization focused on customers, innovation, and responsible practices. The document also notes URC faces competition from companies like Oishi and Nissin but maintains brand loyalty through its product portfolio and corporate social responsibility initiatives.
The document describes an example of using the simplex method to solve a linear programming problem (LPP) for determining the optimal production mix of two products. Specifically, it involves determining the number of cases of men's and women's shampoo a company should produce daily to maximize profits given constraints on available minutes for mixing, bottling, and packing. The simplex method is applied through four steps, arriving at a solution of producing 4 cases of men's shampoo and 8 cases of women's shampoo daily for a total profit of $88 and 14 minutes of unused packing capacity. A second similar example involving classic and decaf coffee production at Nescafe is also presented.
This document provides a summary of insurance, travel, and retail protection benefits available to preferred cardholders. It outlines programs that provide coverage for purchases made on or after April 24, 2014, replacing any previous benefit guides. To file a claim or learn more, call the number provided.
Krishtee Singh Parihar is seeking a position as a quality assurance professional with over 3 years of experience in development quality assurance. She currently works as an Officer of Development Quality Assurance at Plethico Pharmaceuticals Ltd. in Indore, MP, where she is responsible for reviewing documents, monitoring GMP compliance, and coordinating audits. Previously she worked as an Assistant Chemist - Quality Assurance at IPCA Laboratories Limited, where she reviewed batch production and control records. She holds an M.Pharm. in Pharmaceutics from Shri Satya Sai College of Pharmacy and a B.Pharm. from Pt. Ravishankar Shukla University.
PACK-iTS case Analyse and recommendation. short and brief powerpoint presentation .2 slide ppt . discussed inside are the problem , inference and recommendations.
This document contains a chapter summary for a quantitative analysis textbook. It includes 54 multiple choice questions covering topics related to linear programming models, including graphical and computer solution methods. Key topics assessed include formulating linear programming problems, the requirements and assumptions of linear programs, graphical solutions, special cases like infeasibility and redundancy, and sensitivity analysis.
1. The document discusses quantity discount models, including calculating optimal order quantities (Q*) based on setup, holding, and product costs to determine the lowest total cost.
2. It provides examples of applying these models to determine optimal order quantities for various products given annual demand, costs, and discount price structures.
3. The optimal order quantity is the one that results in the lowest total annual cost based on comparing total costs calculated for different possible order sizes.
This document describes a linear programming problem (LPP) to minimize cost. The problem involves determining the optimal amounts of two fertilizer brands, SuperGro and CropQuick, to purchase to minimize total cost while meeting nitrogen and phosphate requirements. The LPP constructs decision variables for amounts of each brand, an objective function to minimize total cost, and constraints on nitrogen and phosphate levels. The optimal solution is to purchase 8 bags of CropQuick for a minimum total cost of 24.
This document presents a case study on supply chain management for Kar Foods. It analyzes the optimal order size for supermarkets with monthly demand of 10,000kg at different unit costs and fixed order costs. With a discount scheme, Kar Foods' profits are 60% higher at an order size of 27,500kg. However, with increased fixed costs, the discount scheme results in worse performance due to higher costs. The document recommends Kar Foods examine their discount rules and consider canceling discounts if needed. It also provides suggestions for Kar Foods such as cooperating with retailers, targeting smaller supermarkets, reducing discounts, and considering minimum order quantities.
Ten principles that form the foundations of financial managementNur Dalila Zamri
The document outlines 10 principles that form the foundations of financial management. The first principle discusses the relationship between risk and return, noting that investors will only take on additional risk if there is potential for higher return. The third principle emphasizes that cash flow, not profits, is most important when evaluating investments as cash indicates when money is actually received. The fifth principle explains that it is difficult to find exceptionally profitable projects due to competition driving down prices and profits over time in efficient markets.
The document discusses sales forecasting techniques for Harmon Foods' breakfast cereal product Treat. It describes wide variability in past sales forecasts, ranging from 50-200% of actual sales. Various factors that influence demand are examined, including seasonality, promotions, and competitor strategies. The case study develops a regression model to forecast sales based on time trends, seasonality, consumer packs, and dealer allowances. Recommendations focus on timing promotions during high seasonal periods and emphasizing more effective dealer allowances over consumer packs.
Managerial Economics - The Organization of the FirmCasey Ordoña
Overview
I. Methods of Procuring Inputs
• Spot Exchange
• Contracts
• Vertical Integration
II. Transaction Costs
• Specialized Investments
• Types of Specialized Investments
Site Specificity
Physical-Asset Specificity
Dedicated Assets
Human Capital
• Implication of Specialized Investment
The document discusses markets for various goods and classifies them as perfectly competitive, monopolistically competitive, or monopolistic. It then analyzes the characteristics of firms in these different market structures and how they determine profit maximizing price and output. The document also provides examples of how individual firms might behave in these market contexts.
Macro Economics_Chapter 7_Consumers,Producers and Efficiency Marketdjalex035
This chapter discusses consumer surplus, producer surplus, and market efficiency. It defines consumer surplus as the difference between what consumers are willing to pay and what they actually pay. Producer surplus is defined as the difference between what producers are paid and their costs. The market equilibrium maximizes the total surplus, which is the sum of consumer surplus and producer surplus. This allocation of resources through supply and demand is efficient because it maximizes the total benefits to both consumers and producers.
The document contains a chapter about project management tools PERT and CPM from a quantitative analysis textbook. It includes 58 multiple choice questions about key concepts related to PERT and CPM, such as their origins and uses, time estimates, critical paths, variances, and probability calculations. The questions test understanding of network diagrams, activity dependencies, slack times, and using PERT and CPM to schedule and manage complex projects.
This document contains 50 multiple choice questions about management science concepts from Chapter 1 of the textbook "Introduction to Management Science, 10e". The questions cover topics like the management science approach, modeling techniques, variables, parameters, data, models, break-even analysis, decision support systems, and linear programming. For each question, the answer, difficulty level, page reference, and keywords are provided.
TruEarth Healthy Foods is considering launching a new line of whole grain pizzas. The document analyzes market research data to determine the potential sales volume of the new product line. It considers customer penetration rates, repeat purchase rates, and sales at different price points. Based on the analysis, the document recommends TruEarth launch the product line, estimating sales of $12.16 million assuming an 11% customer penetration rate and the ability to price between $11.38 to $12.38. Key learnings highlighted are understanding market research assumptions, analyzing data to decide on new products, and recognizing limitations of decisions based on available data.
This document provides an overview of integer programming, goal programming, and nonlinear programming. It begins with learning objectives and an outline of topics to be covered, which include integer programming, modeling with binary variables, goal programming, and nonlinear programming. Several examples are provided to illustrate integer programming problems and how they can be formulated and solved. Mixed-integer and binary variable modeling are explained. Goal programming and how it differs from linear programming in addressing multiple objectives is introduced.
Ann Banks is tasked with launching a new Italian sausage brand for Saxonville Sausage Company to meet profit objectives. She conducts market research through focus groups which reveal customers see Italian sausage as a quick meal solution. Two potential positioning concepts are identified: "Family Connection" and "Clever Cooking". Additional quantitative research shows "Clever Cooking" has higher purchase intent. Banks decides to position the new brand as "Saxonville Italian Sausage" using the "Clever Cooking" territory to appeal to time-strapped mothers. The brand will leverage Saxonville's reputation for quality and emphasize fresh, easy-to-cook attributes.
The document discusses operations research and linear programming. It defines operations research as a scientific approach to determine optimal solutions to decision problems with limited resources. Linear programming problems have decision variables, an objective function to maximize or minimize, and constraints. An optimal solution is a feasible solution that gives the most favorable objective function value. Graphical methods can find the optimal solution by determining the feasible region and optimal point.
This document provides an overview of the Business Finance course for Grade 12 students in the senior high school Academic Track. The course covers fundamental principles of financial management, financial statement analysis, financial planning tools and concepts, sources and uses of funds, basic long-term financial concepts, and an introduction to investments and personal finance. The course is designed to equip learners with skills in financial analysis, planning, and decision-making to help achieve organizational goals. It includes 80 hours of instruction organized into various content areas, with associated learning competencies and performance standards.
The document examines BP's "Beyond Petroleum" branding campaign and response to the 2010 Gulf oil spill from a marketing perspective. It finds that while the branding campaign was initially successful, the spill revealed inconsistencies between BP's brand promise of sustainability and its operations. The summary analyzes BP's crisis response, including its use of social media, finding that while the response was slow at first, BP's later aggressive social media efforts helped restore its damaged brand.
This document provides an overview of Universal Robina Corporation (URC), a major food and beverage company in the Philippines. It discusses URC's history since 1954, current business segments, leadership, goals, and competitive landscape. URC began as a corn milling plant and has since diversified into snacks, beverages, and other food categories. It aims to be the leading brand in the ASEAN region through world-class products and an efficient organization focused on customers, innovation, and responsible practices. The document also notes URC faces competition from companies like Oishi and Nissin but maintains brand loyalty through its product portfolio and corporate social responsibility initiatives.
The document describes an example of using the simplex method to solve a linear programming problem (LPP) for determining the optimal production mix of two products. Specifically, it involves determining the number of cases of men's and women's shampoo a company should produce daily to maximize profits given constraints on available minutes for mixing, bottling, and packing. The simplex method is applied through four steps, arriving at a solution of producing 4 cases of men's shampoo and 8 cases of women's shampoo daily for a total profit of $88 and 14 minutes of unused packing capacity. A second similar example involving classic and decaf coffee production at Nescafe is also presented.
This document provides a summary of insurance, travel, and retail protection benefits available to preferred cardholders. It outlines programs that provide coverage for purchases made on or after April 24, 2014, replacing any previous benefit guides. To file a claim or learn more, call the number provided.
Krishtee Singh Parihar is seeking a position as a quality assurance professional with over 3 years of experience in development quality assurance. She currently works as an Officer of Development Quality Assurance at Plethico Pharmaceuticals Ltd. in Indore, MP, where she is responsible for reviewing documents, monitoring GMP compliance, and coordinating audits. Previously she worked as an Assistant Chemist - Quality Assurance at IPCA Laboratories Limited, where she reviewed batch production and control records. She holds an M.Pharm. in Pharmaceutics from Shri Satya Sai College of Pharmacy and a B.Pharm. from Pt. Ravishankar Shukla University.
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Profit Maximization Case
1. Kevin Rivas
Executive Summary
Angela and Zooey don’t have the necessary funds to have a full menu. To overcome this
challenge they decide to serve two full course meals of either fish or beef. They are trying to decide how
many of dishes of each should they make to add up to 60 meals because that is there maximum
constraint. Angela and Zooey are also trying to decide on whether to increase the price of fish from $12
and whether or not this change in price would affect the current model they have for profit
maximization. They are also trying to decide on whether spending $30 on advertisement which leads to
the amount of meals sold to increase by 10. Also with an unreliable source of labor they want to know
whether or not the reduction in hours would have an effect on the profit level.
Since Angela and Zooey can only make two dishes the profit maximization point between the
fish and beef dishes would be when they make 40 fish meals and 20 beefs meals. At this ratio of dishes
they profit $800. They should also increase the price of the fish meal from $12 to $16 because it would
not affect the number of customers they get since the allowable increase is $4. By charging the same for
fish and beef the profit is $960. The $30 investment in advertisement should also be spent because the
10 added meals results in an $80 profit increase. Lastly we recommend that Angela and Zooey hire a
more reliable labor so that their reduction in hours is less than 5 so that their profit level won’t be
affected.
2. Kevin Rivas
Introduction:
This case involves Angela and Zooey who want to open a French restaurant in Draperton. They
will start off only serving two main dishes. One of them is fish and the other will be beef. The reason
why they only have two dishes is because initially they have no idea the tastes of the locals regarding
French cuisine. They originally expect to be able to sell a maximum of 60 meals each night. Each fish
dinner takes 15 minutes to prepare while each beef dinner takes 30 minutes to prepare. They have a
total of 20 hours of labor in the kitchen each day. They believe that they will sell at a fish to beef ration
of 3 fish for every 2 beef. No matter what, they expect to sell at least 6 beef dinners. Angela and Zooey
expect to make $12 from each fish dinner and $16 from each beef dinner. The analysis asks us to create
a programming model to help estimate the amount of meals they should prepare. The analysis also asks
what effect would an increase in the price of the fish dinner from $12 to $16. Finally, it asks to analyze
the effects on committing 12 beef dinners for each night. The second half of the problem asks us to
solve their problem using the computer rather than by hand. In the second half of the problem we need
to analyze whether or not a $30 cost per day is worth it to sell 70 meals. It also asks to analyze a labor
reduction of five hours effect on the profit level. The final question that needs to be solved is whether or
not increasing the price of the fish dinner to $14 will be best option.
Case Analysis:
A. Key Challenges
Angela and Zooey are opening a restaurant and do not have the funds to have a full menu. They
decide they are going to serve two full course meals with beef and fish. The key challenges for Angela
and Zooey are how many meals they should prepare each night and whether or not they should charge
the same amount of money for each meal. Later on they debate on investing in placing and
advertisement in the newspaper and how much staff they really need to have on board. Lastly, they
debate on if they should raise the price of fish, and wonder if it will affect the demand. They are not sure if
their chef will allow this to happen and how it will affect their profit. Long term they should purchase some
advertising, have less staff, and change the price of fish without affecting the chef’s plans.
3. Kevin Rivas
B. Causes of the Problem
The decision variables in this problem are how many meals of fish and beef to prepare. The quantities to
be produced are representing as:
● x1 = Fish
● x2 = Beef
The linear programming model formulation used is maximize Z = $12x1+16x2. This formula will be used
as an objective function that will maximize the number of meals Angela and Zooey should prepare each
night.
● Z = total profit per day
● $12x1 = profit from fish
● 16x2 = profit from beef
There are numerous model constraints:
Resource Constraints
● x1 + x2 ≤ 60 (maximum meals each night)
● 15x1 + 30x2 ≤ 1200 (labor in minutes to prepare meals) OR
o .25x1 + .50x2 ≤ 20
● 2x1 - 3x2 ≥ 0 (will sell at least 3 fish/2 beef meal) OR
o x1 /x2≥ 3/2
● .90x2 - .10x1 ≥ 0 (at least 10% will order beef) OR
o x2 /(x1+x2) ≤ .10
Non-Negativity
● x1 ≥ 0
● x2 ≥ 0
To solve for the maximum point we will use the graphical solution approach. First we need to plot the
constraints as equations. The lines plotted do not represent the entire constraint; it also includes the
values that are less or equal to the line. The shaded in area on the graph is the feasible solution area
because all the points in this area satisfy all constraints. From the shaded area we can find the optimal
point (B) which is the best feasible solution.
Point B:
4. Kevin Rivas
-20 ≤ -2.86 ≤ Δ ≤ 12.72 ≤ 20
-2.86 ≤ Δ ≤ 12.72
q1 = 60 + Δ Δ+q1 – 60
-26 ≤ q1 -60 ≤12.72
57.14 ≤ q1 ≤ 72.72
● x1 = 40
● x2 = 20
● Z = $800
Point A:
● x1 = 34.3
● x2 = 22.8
● Z = $776.23
Point C:
● x1 = 6
● x2 = 54
● Z = $744
If we were to change the objective function to Z = $16x1 + 16x2 there would be two optimal solutions (B
and C). For both solutions the profit would be $960.
● 16(40) + 16(20) = $960
● 16(6) + 16(54) = $960
If we changed the constraint from 90x2 - .10x1 ≥ 0 to 80x2 - .20x1 ≥ 0 it would have no effect on the
solution because it would not change the optimal point on the graph.
In order to determine if Angela and Zooey should invest in an advertisement we need to look at the
sensitivity range for q1.
S1:
● 40 - 2Δ ≥0
5. Kevin Rivas
If they added 10 meals it would not affect the
shadow price for the mean demand ($800). With
these added 10 meals they would see an increase in
profit of $80. $8 * $10 = $80
The $80 is more than the $30 of advertising so
therefore the Ad should be purchased.
● 7Δ ≥ -40
● Δ ≥ -20
S2:
● 20 – Δ ≥ 0
● Δ ≥ -20
● Δ ≤ 20
S3:
● 20 + 7Δ ≥ 0
● 7Δ ≥-20
● Δ ≥ -2.86
S4:
● 14 – 1.1Δ ≥ 0
● 1.1Δ ≥ -14
● Δ ≤ 20
If they have a night where they have a staff reduction as much as 5 hours it would affect their profit
level in a negative way. Based on the Sensitivity Report we can see that the shadow price is 16 and
therefore anything less than that would be unacceptable.
Based on the Sensitivity Report we can see that Angela and Zooey could increase their price by as much
as $4. So raising the price from $12 to $14 would be acceptable to Pierre and there would be and $80
profit per night.
Original profit: $800
New profit: (14 * 40)+ (16*20) = $880 $880 - $800 = $80
C. Evaluation: Decision criteria and Alternative solutions
The decisions in which Angela and Zooey have to choose from for the chapter 2 problem are whether or
not making the profit from both dinners the same would have an effect on their solution and what
6. Kevin Rivas
effect would allocating 20% of the dinners to beef rather than 10% have on their meal preparation plan.
The solutions for the first half of the problem regarding the profit for both dinners would to keep the
price the same and have a profit of $800 or change the prices to both be $16 and have a profit of $960.
The solutions for the second half of the problem are to keep 10% allocated for beef or to allocate 20%
for beef. It turns out that both of the solutions are the same.
The decision in which Angela and Zooey have to choose from for chapter 3 are whether or not to
advertise, whether or not a reduction in 5 hours of labor will affect their profit level, and whether or not
raising the price of the fish dinner to $14 would be acceptable to Pierre (their Chef) and how much profit
it would earn them. The solutions to whether or not they should advertise are not advertising and make
what they are making right now, or to advertise and gain 10 meals which would increase profit by
$50($80-$30). The solutions to whether or not a decrease in labor available by 5 hours would affect
profit is to keep doing what they are doing or reduce labor. Reducing their labor to anything less than 16
would result in losing profit. Finally, the solutions regarding whether or not to change the price of fish to
$14 are to keep the price at $12 or change it to $14. Keeping the price at $12 would yield profit of $800
while changing the price would yield a profit of $880.
Recommended Solution
Angela and Zooey should serve 40 fish meals and 20 beef meals per night, this is the quantity at which
profit is maximized (when price of fish=12 and price of beef=16, profit=800). We also recommend
increasing the price of fish to $16. By charging the same amount for both meals profit rises from $800 to
$960 ( 40*16 + 20*16 = 960).
Advertising will add 10 more meals per night and increase profit by $80, this increased profit is larger
than the $30 cost of advertising so the newspaper ad should be purchased. More reliable staff should be
hired in the long run. If labor is reduced by 5 hours it will fall to 15 hours, this is below the point at which
profit will be negatively affected (16 hours). In order to keep their profit where it is they cannot afford to
reduce labor. Changing the price of fish to $14 will increase profit by $80, which is acceptable to the
chef. But we recommend increasing the price to $16, this will grant an additional $80 of profit.