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# Product design & selection process problems solution

Production & operation Managemtent
Solution of Chapter # 3

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### Product design & selection process problems solution

1. 1. University Of central Punjab F14 Production & Operation Management Page 1 Subject: Production & Operation Management Topic: Solve problems Assignment No: 2 Submitted To: Sir Usman Waris Submitted By: Ayesha Hamid
2. 2. University Of central Punjab F14 Production & Operation Management Page 2 Question No 1. See-Clear Optics is considering producing a new line of eyewear. After considering the costs of raw materials and the cost of some new equipment, the company estimates axed costs to be \$40,000 with a variable cost of \$45 per unit produced. a) If the selling price of each new product is set at \$100, how many units need to be produced and sold to break even? Use both the graphical and algebraic approach? b) If the selling price of the product is set at \$80 per unit, See-Clear expects to sell 2000 units. What would be the total contribution to profit from this product at this price? c) See-Clear estimates that if it offers the price at the original target of \$100 per unit, the company will sell about 1500 units. Will the pricing strategy of \$100 per unit or \$80 per unit yield a higher contribution to port? Solution (a) Fixed Cost= \$40000 Variable Cost= \$ 45 per unit Selling Price= \$100 Break Even Quantity = Fixed Cost Selling price per unit − Variable cost per unit Break Even Quantity = \$40000 \$100 − \$45 Break Even Quantity = \$40000 \$55 Break Even Quantity = 728 units (b) Selling Price= \$80 Expected Sales (Q) = 2000 units Contribution to Profit= Total Revenue – Total Cost Contribution to Profit= SP (Q) – [FC+VC (Q)] Contribution to Profit= \$80(2000) – [\$40000+\$45(2000)]
3. 3. University Of central Punjab F14 Production & Operation Management Page 3 Contribution to Profit= \$30000 (c) Selling Price= \$100 Expected Sales= 1500 units Contribution to Profit= Total Revenue – Total Cost Contribution to Profit= SP (Q) – [FC+VC (Q)] Contribution to Profit= \$100(1500) – [\$40000+\$45(1500)] Contribution to Profit= \$42500 Conclusion: Pricing strategy of \$100 per unit yield a higher contribution to profit. Question No 2. Med-First is a medical facility that offers outpatient medical services. The facility is considering offering an additional service, mammography screening tests on site. The facility estimates the annual fixed cost of the equipment and skills necessary for the service to be \$120,000. Variable costs for each patient processed are estimated at \$35 per patient. If the clinic plans to charge \$55 for each screening test, how many patients must it process a year in order to break even? Solution Fixed cost = F.c = \$ 12,000 Variable cost = V.C = \$ 35 Charges = Selling price = S.P = \$55 No. of patients for break even = Q (BE) =? Patients (B.E) Break Even Quantity = Fixed Cost Selling price per unit − Variable cost per unit Break Even Quantity = 12000 / (55-35) Break Even Quantity = 6000 Patients Question No 3. Tasty Ice Cream is a year-round take-out ice cream restaurant that is considering offering an additional product, hot chocolate. Considering the additional machine it would need plus cups and ingredients, it estimates fixed cost per year to be \$200 per year and the variable cost at \$.20. If it charges \$1.00 for each hot chocolate, how many hot chocolates does it need to sell in order to break even? Solution Fixed cost = \$ 200 Variable cost = \$ 1
4. 4. University Of central Punjab F14 Production & Operation Management Page 4 Selling price = \$ 0.2 Breakeven = QB.E = F.c / S.p – v.c QB.E = 200/ 1 – 0.2 = 250 hot chocolates Question No 4 Slick Pads is a company that manufactures laptop notebook computers. The company is considering adding its own line of computer printers as well. It has considered the implications from marketing and financial perspectives and estimates fixed costs to be \$500,000. Variable costs are estimated at \$200 per unit produced and sold. (a) If the company plans to offer the new printers at a price of \$350, how many printers does it have to sell to break even? (b) Describe the types of operations considerations that the company needs to consider before making the final decision. Fixed cost = F.c = \$ 500,000 Variable cost = V.C = \$ 200 Selling price = S.P = \$ 350 Q (BE) = F .C / (S.P – V.C) Solution (a) Q (BE) = 500000 / (350 – 200) = 3333 units (b) Early and later stage of product life cycle operation. Delivery, flexibility, cost and quality operation. Resources grouped by function, and function arranged in a line operation. Make to stock, make to order or assemble to order prearranged in a line operation. Low and high operation. Question No 5 Perfect Furniture is a manufacturer of kitchen tables and chairs. The company is currently deciding between two new methods for making kitchen tables. The first process is estimated to have a fixed cost of \$80,000 and a variable cost of \$75 per unit. The second process is estimated to have a fixed cost of \$100,000 and a variable cost of \$60 per unit. (a) Graphically plot the total costs for both methods. Identify which ranges of product volume are best for each method. (b) If the company produces 500 tables a year, which method provides a lower total cost?
5. 5. University Of central Punjab F14 Production & Operation Management Page 5 Solution Process 1 Fixed Cost= \$80000 Variable Cost=\$75 per unit Process 2 Fixed Cost=\$100000 Variable Cost= \$60 per unit a) …. b) Quantity=500 units Process 1 Total Cost= Fixed Cost +Variable Cost TC=FC+VC (Q) TC= \$80000 + (75) (500) TC=\$117500 Process 2 Total Cost= Fixed Cost +Variable Cost TC=FC+VC (Q) TC= \$100000 + (60) (500) TC=\$130000 Conclusion: Process 1 provides a lower total cost.
6. 6. University Of central Punjab F14 Production & Operation Management Page 6 Question No 6 Harrison Hotels is considering adding a spa to its current facility in order to improve their list of amenities. Operating the spa would require a fixed cost of \$25,000 a year. Variable cost is estimated at \$35.00 per customer. The Hotel wants to break even if 12,000 customers use the spa facility. What should be the price of the spa services? Solution Fixed cost = F.c = \$ 25,000 Variable cost = V.C = \$ 35 Customer (BE) = 12,000 Selling price = S.P =? Q (BE) = F .C / (S.P – V.C) 12,000 = 25,000 / S.P – 35 25000/12000 = S.P – 35 2.083 = S.P – 35 S.P = 35 + 2.083 S.P = \$ 37.083 Question No 7. KaizerPlasticsproducesavarietyof plasticitemsforpackaginganddistribution.One item, container#145, has had a lowcontributiontoprofits.Lastyear,20,000 unitsof container#145 were producedandsold.The sellingprice of the containerwas\$20.00 perunit,witha variable cost of \$18 per unitanda fixedcostof \$70,000 per year. (a) What is the break-evenquantityforthisproduct?Use bothgraphicand algebraicmethodsto getyour answer. (b) The companyis currentlyconsideringwaysto improve profitabilitybyeitherstimulating salesvolumesorreducingvariablecosts.Managementbelievesthatsalescanbe increasedby 35 percentof theircurrentlevelsorthatvariable costcan be reducedto90 percentof their currentlevel.Assuming all othercostsequal,identifywhichalternative wouldleadtoahigher profitcontribution. Solution Fixed Cost=\$70000 Variable Cost=\$18 per unit Selling Price=\$20 per unit a) Break Even Quantity = Fixed Cost Selling price per unit − Variable cost per unit Break Even Quantity = \$70000 \$20 − \$18
7. 7. University Of central Punjab F14 Production & Operation Management Page 7 Break Even Quantity = 35000 units b) Increase in Sales=35% Increased Sales= 20000(1.35) = 27000 units Contribution to Profit= Total Revenue – Total Cost Contribution to Profit= SP (Q) – [FC+VC (Q)] Contribution to Profit= \$20(27000) – [\$70000+\$18(27000)] Loss= \$16000 Reduce in Variable Cost= 90% Reduced Variable Cost=18(0.90) =\$16.20 Contribution to Profit= Total Revenue – Total Cost Contribution to Profit= SP (Q) – [FC+VC (Q)] Contribution to Profit= \$20(20000) – [\$70000+16.20(20000)] Contribution to Profit= \$6000 Conclusion: Reducing variable cost is more beneficial for the company. Question No 8. George Fine, owner of Fine Manufacturing, is considering the introduction of a new product line. George has considered factors such as costs of raw materials, new equipment, and requirements of a new production process. He estimates that the variable costs of each unit produced would be \$8 and fixed cost would \$70,000. (a) If the selling price is set at \$20 each, how many units have to be produced and sold for Fine Manufacturing to break even? Use both graphical and algebraic approaches.
8. 8. University Of central Punjab F14 Production & Operation Management Page 8 (b) If the selling price of the product is set at \$18.00 per unit, Fine Manufacturing expects to sell 15,000 units. What would be the total contribution to profit from this product at this price? (c) Fine Manufacturing estimates that if it offers the price at the original target of \$20 per unit, the company will sell about 12,000 units. Which pricing strategy–\$18.00 per unit or \$20.00 per unit–will yield a higher contribution to profit? (d) Identify additional factors the George Fine should consider in deciding whether to produce and sell the new product. Additional line of services to include professional office cleaning. Annual fixed costs for this additional service are estimated to be \$9,000. Variable costs are estimated at \$50.00 per unit of service. If the price of the new service is set at \$80.00 per unit of service, how many units of service are needed for Handy-Maid to break even? Solution (a) Fixed Cost=\$70000 Variable Cost=\$8 per unit Selling Price=\$20 per unit Break Even Quantity = Fixed Cost Selling price per unit − Variable cost per unit Break Even Quantity = \$70000 \$20 − \$8 Break Even Quantity = 5833 units (b) Selling Price=\$18 per unit Estimated Sales=15000 units Contribution to Profit= Total Revenue – Total Cost Contribution to Profit= SP (Q) – [FC+VC (Q)]
9. 9. University Of central Punjab F14 Production & Operation Management Page 9 Contribution to Profit= \$18(15000) – [\$70000+\$8(15000)] Contribution to Profit= \$80000 (c) Selling Price=\$20per unit Estimated Sales=12000 units Contribution to Profit= Total Revenue – Total Cost Contribution to Profit= SP (Q) – [FC+VC (Q)] Contribution to Profit= \$20(12000) – [\$70000+\$8(12000)] Contribution to Profit= \$74000 Conclusion: Pricing strategy of \$18 per unit will yield higher contribution to profit. Question No 9 Handy Maid Cleaning service is considering offering an additional line of service to include professional office cleaning. Annual fixed costs for this additional service are estimated to be \$9000. Variable costs are estimated at \$50 per unit of service. If the price of the new service is a set at \$80 per unit of service, how many units of service are needed for Handy Maid to break even? Solution Variable Cost=\$50 Selling Price=\$80 Fixed Cost=\$70000 Break-even Quantity= Fixed Cost / (Selling Price- Variable Cost) Break-even Quantity = 9000/ (80- 50) Break-even Quantity =300 units of service Question No 10. Easy-Tech Software Corporation is evaluating the production of a new software product to compete with the popular word processing software currently available. Annual fixed costs of producing the item are estimated at \$150,000 while the variable costs are \$10.00 per unit. The current selling price of the item is \$35.00 per unit, and the annual sales volume is estimated at 50,000 units. (a) Easy-Tech is considering adding new equipment that would improve software quality. The negative aspect of this new equipment would be an increase in both fixed and variable costs. Annual fixed cost would increase by \$50,000 and variable cost by \$3.00. However, marketing expects the better quality product to increase demand to 70,000 units. Should
10. 10. University Of central Punjab F14 Production & Operation Management Page 10 Easy-Tech purchase this new equipment and keep the price of their product the same? Explain your reasoning. (b) Another option being considered by Easy-Tech is the increase in the selling price to \$40.00 per unit to offset the additional equipment costs. However, this increase would result in a decrease in demand to 40,000 units. Should Easy-Tech increase their selling price if they purchase the new equipment? Explain your reasoning Fixed cost = F.c = \$ 150,000 Variable cost = V.C = \$ 10 per unit Selling price = S.P = \$ 35 Quantity sold = Q = 50,000 units Solution (a) New Fixed Cost = \$ 200,000 New Variable cost = V.C = \$ 13 Quantity Sold = Q = 70,000 Contribution to profit at old process = C.T.P = TR – TC TR = 50000 × 35 = 1,750,000 TC = F.C + V.C (Q) TC = 15000 + 10(50000) = 650000 C.T.P = TR – TC C.T.P = 1750000 – 650000 = \$ 1,100,000 Contribution to profit with new process TR = 70000 × 35 = \$ 2,450,000 TC = F.C + V.C (Q) TC = 200000 + 13(70000) = 1,110,000 C.T.P = TR – TC C.T.P = 245000 – 1110000 = \$ 1,340,000 So, new process is more profitable. (b) Selling price = S.P = \$ 40 Quantity sold = 40,000 Contribution to profit C.T.P = TR – TC TR = 40(40000) = \$ 1,600,000 TC = 1,110,000 C.T.P = TR – TC C.T.P = 160000 – 111000 = \$ 4, 90,000 Profitability decrease 1,340,000 to 4, 90,000. So, easy tech should not increase its selling price at purchasing of new equipment.
11. 11. University Of central Punjab F14 Production & Operation Management Page 11 Question No 11. Zodiac Furniture is considering the production of a new line of metal office chairs. The chair can be produced in -house using either process A or process B. The chairs can also be purchased from an outside supplier. Specify the levels of demand for each processing alternative given the cost in the table. Fixed Cost Variable Cost Process A \$ 20000 \$ 30 Process B \$ 30000 \$ 15 Outside Supplier \$ 0 \$ 50 Solution Indifference Quantity between Process A and Process B Total Cost A= Total Cost B [FC+ VC (Q)]A= [FC+ VC (Q)]B The equation rearranges to: Q = (FCB- FCA)/ (VCA- VCB) Q = (30000- 20000)/ (30- 15) Q = 666.7, or 667 chairs. Process A is better than Process B when demand is below 667 chairs. Indifference Quantity between Process A and Outsourcing Total Cost A = Total Cost O [FC+ VC (Q)]A= [FC+ VC (Q)]O Q = 20000/ (50-30) = 1000 chairs Process A is better than outsourcing when demand is over 1000 chairs. Indifference Quantity between Process B and Outsourcing Total Cost B = Total Cost O [FC+ VC (Q)]B = [FC+ VC (Q)]O Q = 30000/ (50- 15) Q = 875.14, or 857 chairs. Process B is better than outsourcing when demand is over 857 chairs.
12. 12. University Of central Punjab F14 Production & Operation Management Page 12 In summation: Demand Ranges Cheapest Production 0 to 857 Outsourcing 858 and more Process B Process A is never the best alternative. Question No 12. Mop and Broom Manufacturing is evaluating whether to produce a new type of mop. The company is considering requirements for the mop as well as the market potential. Estimates of fixed cost per year are \$ 40,000, and the variable cost for each mop produced is \$20. (a) If the company sells the product at a price of \$ 25, how many units of product have to be sold in order to break even? Use both the algebraic and graphical approaches. (b) If the company sells 10,000 mops at the product price of \$ 25, what will be the contribution to profit? Solution (a) Fixed Cost= \$40000 Variable Cost=\$20 per unit Selling Price=\$25 per unit Break Even Quantity = Fixed Cost Selling price per unit − Variable cost per unit Break Even Quantity = \$40000 \$25 − \$20 Break Even Quantity = 8000 units
13. 13. University Of central Punjab F14 Production & Operation Management Page 13 (b) Units Sold=10000 Selling Price=\$25 per unit Contribution to Profit= Total Revenue – Total Cost Contribution to Profit= SP (Q) – [FC+VC (Q)] Contribution to Profit= \$25(10000) – [\$40000+\$20(10000)] Contribution to Profit= \$10000 Question No 13. Mop and Broom Manufacturing, from Problem 12, has decided to produce a new type of mop. The mop can be made with the current equipment in place. However, the company is considering the purchase of new equipment that would produce the mop more efficiently. The fixed cost would be raised to \$ 500000 per year, but the variable cost would be reduced to \$ 15 per unit. The company still plans to sell the mops at \$ 25 per unit. Should Mop and Broom produce the mop with the new or current equipment described in problem 12? Specify the volume of demand for which you would choose each process. Solution It is known from Problem 12, that money is lost if demand is under 8,000 units; Breakeven between old and new equipment; Fixed cost = 50,000 Variable cost= 15 Selling price = 25 FC0 + VC0 (Q) = Fan + Van (Q) 40,000+ 20(Q) = 50,000 + 15(Q) 20Q – 15Q = 50,000 – 40,000 5Q = 10,000 Q = 10,000 / 5 Q = 2,000 Use the old equipment if demand is at most 2,000 units. Use the new equipment if demand is over 2,000 units. Question No 14. Jacob’s baby food company must go through the following steps to make mashed carrots: (1) Unload carrots from truck (2) Inspect Carrots (3) Weigh carrots (4) Move to storage
14. 14. University Of central Punjab F14 Production & Operation Management Page 14 (5) Wait until needed (6) Move to washer (7) Boil in water (8) Mash carrots (9) Inspect Draw a process flow die gram for these steps. Solution Question No 15. Draw a process flow diagram of your last doctor’s office visit. Identify bottlenecks. Did any activities occur in parallel? Solution Bottlenecks occur during the waiting period. Parallel activities such as lab results or X- rays may be analyzed during some of the waiting times.
15. 15. University Of central Punjab F14 Production & Operation Management Page 15 Question No 16 Oakwood Outpatient Clinic is analyzing its operation in an effort to improve performance. The clinic estimates that a patient spends on average 3 ½ hours at the facility. The amount of time the patient in contact with staff is estimated at 40 minutes. On average the facility sees 42 patients per day. Their standard has been 40 patients per day. Determine process velocity and efficiency for the clinic. Solution Average estimated time spend = 3.5 hours Contact Time = 40 minutes No. patients facilitated = 42 patients No. of standard patients = 40 patients Process velocity = Estimated Time / Time Spend Process velocity = 210 / 40 = 5.25 Efficiency of clinic = Patients facilitated / standard × 100 Efficiency of clinic = 42 / 40 × 100 = 105% Question No 17. Oakwood Outpatient Clinic rents a magnetic resonance imaging (MRI) machine for 30 hours a month for use on its patients. Last month the machine was used 28 hours out of the month. What was the machine utilization? Solution Used time of machine = 28 hours Available time of machine= 30 hours Utilization = used time / available time Utilization = 28 / 30 *100% Utilization = 93.3% Question No 18. Mop and Broom Manufacturing estimates that it takes 4 ½ hours for each broom to be produced, from raw material to final product. An evaluation of the process reveal that the amount of time spent working on the product is 3 hours. Determine process velocity. Solution Estimating taking hours = 4.5 hours Evolution time spend = 3 hours Process velocity = Estimated time / Time spend Process Velocity = 4.5 / 3 = 1.5 hours
16. 16. University Of central Punjab F14 Production & Operation Management Page 16
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Production & operation Managemtent Solution of Chapter # 3

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