This document discusses quantitative methods for decision making, also known as operations research. It defines decision making as the process of choosing among alternatives. The document then discusses different types of decisions, such as sequential, conscious/unconscious, and managerial decisions. It also discusses various farm management decisions including organizational, administrative, and marketing decisions. Finally, it provides an example of using linear programming to solve a problem involving maximizing profit from toy production given resource constraints.

1. Presented by
Ravi Kumar Rathiya
M.Sc. (Ag.) Previous
Depart. Of Agril. Economics
Presentation
on

2. Decision making can be defined as the
process of making choices among the
possible alternatives. The skills considered
important to effective decision making are
based on a normative model of decision
making, which prescribes how decisions
should be made.

3.  Sequential decisions:- Decisions in which the outcome of the
decisions influences other decisions are known as sequential decisions.
For example, a company trying to decide whether or not to market a
new product might first decide to test the acceptance of the product
using a consumer panel.
 Conscious or unconscious decisions:- These decisions are taken
under consciousness or unconsciousness.
 Managerial decisions:- Decisions concerning the operation of the
firm, such as the choice of the farm size, firm growth rate, and
employee compensation are known as Managerial Decisions.
 Farm Management decisions:- Farm management implies decision
making process. Several decisions need to be made by the farmer as a
manager in the organizational management decisions.

4. These are some types of Farm Management decisions.
a. Organizational Management decisions:- The
Organizational management decisions are further sub-
divided into operational management decisions and
strategic management decisions.
b. Administrative Management Decisions:- Beside organizational
management decisions, the farmer also make some administrative
decisions like financing the farm business, supervision, accounting
and adjusting his farm business according to government policies.
c. Marketing Management Decisions:- Marketing decisions are most
important under changing environment of Agriculture. These
decisions include buying and selling.

5. There are some types of Organizational Management decision
a. operational Management Decisions:-
 Those decisions which involve less investment and are made frequently, are
called operational management decisions.
 These decisions can be reversed without incurring a cost or less cost.
 Decisions like; what to produce? How to produce? How much to produce?
are some of important operational management decisions.
b. Strategic Management Decisions:-
 These decisions involves heavy investment and are made less frequently.
 The effect of these decisions is long lasting.
 These decisions can not be altered.
 These decisions are also known as basic decisions.
 Example:- Size of farm, construction of farm building.

6. INTRODUCTION
The area of quantitative methods for decision making is
based on the scientific method for investigating and
helping to take decisions about complex problems in
modern organizations. Quantitative methods for decision
making are also known as operations research.

7. 1. To describe the quantitative analysis approach.
2. To understand the application of quantitative analysis
in a real situation.
3. To describe the use of modelling in quantitative
analysis.
4. Use computers and spreadsheets models to perform
quantitative analysis.
5. Discuss possible problems in using quantitative
analysis.
6. To perform a break even point.

8. 1. Clear study questions or hypothesis.
2. Logical sequence and smooth flow of questions.
3. Formal conducive to efficient, clear and compete
recording of responses.
4. Sound sampling procedures that will generate
representative samples of clients.

9.  Quantitative analysis are a scientific approach to managerial
decision making whereby row data are processed and
manipulated resulting in meaningful formulation
 Quantitative analysis is applied to variety of problems.
Mathematical tools have been used from thousand of years.
 Quantitative factors might be different, investment alternatives,
interest rates, inventory levels or labour cost.
 Qualitative factors such as weather, state and federal legislation
and technology break throw should also be considered.
manipulated resulting in meaningful formulation

10. Defining the
problem
Developing a
Model
Acquiring
input data
Developing a
solution
Testing the
solution
Analyzing the
results
Implementing
the results

11. 1. Defining the problem:-
 It need to develop a clear and statement that give direction and
meaning to the following steps.
 It is essential to go beyond the symptoms and identify the true
causes.
 May be necessary to concentrate on only a few of the
problems; selecting the right problems is very important.
2. Developing a model:-
 Quantitative analysis models are realistic, solvable and
understandable mathematical representation of a situation.
They generally contain variables.
3. Acquiring input data:-
 Data may come from variety of sources such as company
reports, sampling etc. Meaningful data is processed

12. 4. Developing a solution:-
 The best(optimal) solution to a problem is found by
manipulating the model variable until a solution is found that is
practical and can be implemented.
5. Testing the solution:-
 Both input data and the model should be tested for accuracy
before analysis and implementation.
 Aif it is found good after testing then only it can be
implemented.
6. Analysing the results:-
 After testing the results should be carefully analysed so that
implementation can be done more accurately.
7. Implementation of the results:-
 Now the results are implemented.

13.  We know that profit is equal to revenue minus total cost.
 Total cost is fixed cost plus variable cost so the mathematical equation will be
 Profit = Revenue – (Fixed cost + Variable cost)
 Now Revenue is equal to selling price per unit multiplied by Number of units sold,
so the equation becomes-
 Profit = (selling price/unit) (number of units sold) – (Fixed cost + Variable cost/
unit)
 Profit = S X – ( f t v x)
 Where ,
 S = Selling price per unit.
 V = Variable cost per unit.
 f = Fixed cost.
 X = Number of units.

14. 1. Models can represent reality vary accurately.
2. Models can help a decision maker to formulate problems.
3. Models can give us insight and information.

15. Introduction
 The term ‘Linear’ is used to describe the proportionate
relationship of two or more Variables in a model. The given
change in one variable will always cause a resulting Proportional
change in another variable
 .The word , ‘programming’ is used to specify a sort of
planning that involves the economic allocation of limited
resources by adopting a particular course of action or strategy
among various alternatives strategies to achieve the desired
objective.
 Linear Programming is a mathematical technique for optimum
allocation of limited or Scarce resources, such as labour, material,
machine, money, energy and so on, to several Competing
activities such as products, services, jobs and so on, on the basis
of a given Criteria of optimality.

16. The basic structure of an LP problem is either to maximize or minimize an objective
function, while satisfying a set of constraining conditions called constraints.
1. . Objective function:-
 The objective function is a mathematical representation of the overall goal stated in
terms of the decision variables. The firm’s objective and its limitations must be
expressed as mathematical equations or inequalities, and these must be linear equations
and inequalities.
1. Constraints:-
 Constraints are also stated in terms of the decision variables, and represent conditions
which must be satisfied in determining the values of the decision variables. Most
constraints in a linear programming problem are expressed as inequalities. They set
upper or lower limits, they do not express exact equalities; thus permit many
possibilities.
1. Decision variables:-
 Decision variables are the unknown quantities in the linear which will achieve the
objective. programming formulations

17. Linearity:- The objective function and constraints are all linear functions;
that is, every term must be of the first degree. Linearity implies the next
two assumptions. It implies the products of two variables such as X1X2,
powers of variables such as x2 , combination of variables such as- ax1 +
2.5x2 = 5000
Proportionality:- For the entire range of the feasible output, the rate of
substitution between the variables is constant. It means that profit per unit
is directly proportional to number of units sold.
Additivity:- All operations of the problem must be additive with respect to
resource usage, returns, and cost. This implies independence among the
variables.
Divisibility:- Non-integer solutions are permissible. It implies the care of
products and resources to be used.
Certainty:- All coefficients of the LP model are assumed to be known with certainty.
Remember, LP is a deterministic model.
Multiplicativity:- If we take one hour on a single item on a given machine it take ten
hours to make ten parts. The total profit by selling given number of units of a
product is the unit profit multiplied by the number of units sold.

18. Machine assignment problems:-The transportation has been used with considerable success to solve
certain type of machine assignment problems.
Regular time and over time production:-The problem of scheduling regular and over time production
can some times be solved with help of transportation method or linear programming.
Optimal product mix and activity levels:-We wish to consider practical problems which , when
formulated, become general linear programming problems rather than transportation types of
problems, and have to be solved by simplex algorithm or one of the other general algorithm.
Petroleum refinery operations:-In recent years, many petroleum companies have made efforts to
optimise refinery operations by means of linear programming.
Blending problems:-In general, blending problems refer to situations where a number of components
are mixed together to yield one or more products. These types of problems are solved with the help
of Linear Programming.
Standard Transpiration problems:-These problems seek to minimise those costs incurred from
shipping a uniform product available in given amount at m origins to n destination where the amount
at each destination is also specified.
Linear Programming application in firms:- The Linea Programming model make it possible to permit
the firm to produce a number of products which jointly use the production facilities.

19. 1. Solve the business problems:- With linear programming we can easily
solve business problems. It is very benefited to increase the profit or
decrease the cost.
2. Easy work of Manager under limitations and conditions:- Linear
Programming solve problems under different limitations and conditions, so
that it is easy for manager to work under limitations and conditions.
3. Use in solving staffing problems:- With the help of Linear Programming
we can calculate the number of staff needed in hospitals, mines, hotels and
other type of business.
4. Select best advertising media:- With the help of Linear Programming we
can select best advertising media among the number of media.
5. Best use of available resources:- Best use of scarce resources is a
challenge in front of firms which can be achieved by Linear Programming.

20. PROBLEM 1
A small factory produces two types of toys: trucks and
bicycles. In the manufacturing process two machines
are used: the lathe and the assembler. The table shows the
length of time needed for each toy:
The lathe can be operated for 16 hours a day and there are
two assemblers which can each be used for 12 hours a day.
Each bicycle gives a profit of £16 and each truck gives a
profit of £14. Formulate and solve a linear programming
problem so that the factory maximises its profit.

21. Time on
lathe (hours)
Time on
assembler (hours)
Bicycle 2 2
Truck 1 3
Step 1. Define all decision variables.
Let X= number of bicycles made
Y = number of trucks made.
Step 2. Define the objective function.
Maximise P = 16x + 14y
Step 3. Define all constraints.
2x + y ≤ 16 Lathe
2x + 3y ≤ 24 Assembler
x , y  0 (non-negativity requirement)

22. Step 4. Graph all constraints
Step 5. Determine the area of feasible solutions.
For Steps 4 and 5, please refer to the following graph

23. Step 6. Determine the optimal solution.
Using the shot-gun approach, we list down the following corners or
extreme points (with their respective coordinates):
X = 8 y = 16 P = 16 (8) + 14(16) = 142
X = 12 y = 8 P = 16 (12) + 14 (8) = 304
The Optimal Solution
Step 7. Determine the binding and non-binding constraints.
Observing graphically, Optimal solution is to make 6 bicycles and 4
trucks. Profit £152

24. PROBLEM 2
Alpha ltd. produces two products X and Y each requiring same
production capacity. The total installed production capacity is 9
tones per days. Alpha Ltd. Is a supplier of Beta Ltd. Which must
supply at least 2 tons of X & 3 tons of Y to Beta Ltd. Every day.
The production time for X and Y is 20 machine hour pr units &
50 machine hour per unit respectively the daily maximum
possible machine hours is 360 profit margin for X & Y is Rs. 80
per ton and Rs. 120 per ton respectively. Formulate as a LP
model and use the graphical method of generating the optimal
solution for determining the maximum number of units of X &
Y, which can be produced by Alpha Limited.

25. SOLUTION
Step 1. Define all decision variables.
x1 = Number of units ( in tones ) of Product X.
x2 = Number of units ( in tones ) of Product Y.
Step 2. Define the objective function.
Maximize (total profit) Z = 80 X1 + 120 X2
Step 3. Define all constraints.
X1 + X2 ≤ 9, X1 ≥ 2, X2 ≥ 3 (Supply constraint)
20 X1 + 50 X2 ≤ 360 (Machine hours constraint)
and
X1 ≥ , X2 ≥ 0 (non-negativity requirement)
Step 4. Graph all constraints.

26. Step 5. Determine the area of feasible solutions. For Steps 4 and 5, please refer to the
following graph

27. Step 6. Determine the optimal solution.
Now the region of feasible solution shown in the following figure
is bounded by the graphs of the Linear equalities
X1 + x2 = 9,
x1 = 2,
x2 = 3 and
20x1 + 50x2 = 360 and by the coordinates axes

28. The corner points of the solution space are:
A(2,6.4), B (3,3),(6,3) and D(2,3)
The value of the objective function at these corner points
can be determined as follows:
Corner Points Co-ordinates of
Corner Points (
x1, x2)
Objective
Function
Z=80x1+20x2
Value
A (2,6.4) (80(2) +120(6.4) 928
B (3,6) (80(3) +120 (6) 960
C (6,3) (80(6) +120(3) 840
D (2,3) (80(2) +120(3) 520
Corner Points Co-ordinates of
Corner Points (
x1, x2)
Objective
Function
Z=80x1+20x2
Value
A (2,6.4) (80(2) +120(6.4) 928
B (3,6) (80(3) +120 (6) 960
C (6,3) (80(6) +120(3) 840
D (2,3) (80(2) +120(3) 520

29. Step 7. Determine the binding and non-binding constraints.
Observing graphically,
The maximum profit ( value of Z) of Rs. 960 is found at
corner point B i.e., x1=3 and x2 = 6. Hence the company
should produce 3 tones of product X and 6 tones of
product Y in order to achieve a maximum profit of Rs.
960.