DOMS304 APPLICATIONS OF OPERATIONS RESEARCH FEB MARCH 2025

Description

SESSION	FEB-MAR 2025
PROGRAM	MASTER OF BUSINESS ADMINISTRATION (MBA)
SEMESTER	3
course CODE & NAME	doms304 Applications of Operations research

 

 

Assignment Set – 1

 

 

Q1. A furniture dealer deals only two items viz., tables and chairs. He has to invest Rs.10,000/- and a space to store atmost 60 pieces. A table cost him Rs.500/– and a chair Rs.200/–. He can sell all the items that he buys. He is getting a profit of Rs.50 per table and Rs.15 per chair. Formulate this problem as an LPP, so as to maximize the profit.

Ans 1.

LPP Formulation for the Furniture Dealer Problem

Step 1: Define the Decision Variables

Let:  = number of tables to be bought  = number of chairs to be bought

Step 2: Objective Function (Profit Maximization)

The dealer earns:

• 50 profit per table
• 15 profit per chair

So, the total profit (Z) is:

or maximizing the profit for the furniture dealer.

Its Half solved only

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Q2. Discuss the assumptions of linear programming.

Ans 2.

Assumptions of Linear Programming

Linear Programming

Linear Programming (LP) is a mathematical technique used for optimal allocation of limited resources to achieve a specific objective, such as maximizing profit or minimizing cost. It is widely applied in business, manufacturing, logistics, and other operational areas where decision-making involves constraints. However, the accuracy and effectiveness of a linear programming model depend on several underlying assumptions. These assumptions simplify real-world problems into a solvable linear structure and help define the boundaries within

 

 

Q3. Solve the following LPP using simplex method.

Maximize Z = 70x₁ + 50x₂

Subject to:        4x₁ + 3x₂ ≤ 240

                          2x₁ + x₂ ≤ 100

                                                                           and x₁, x₂ ≥ 0

 

Ans 3.

Problem is

Max Z = 70 x1 + 50 x2

subject to

4 x1 + 3 x2 ≤ 240 2 x1 + x2 ≤ 100

and x1,x2≥0;

The problem is converted to canonical form by adding slack, surplus and artificial variables as appropiate

1. As the constraint-1 is of type ‘≤’ we should add slack variable S1
2. As the constraint-2 is of type ‘≤’ we should add slack variable S2

After introducing slack variables

Max Z = 70 x1 + 50 x2 + 0 S1 + 0 S2

subject to

 

 

 

Assignment Set – 2

 

4. A computer centre has four expert programmers and need to develop four application programmes. The head of the computer centre, estimates the computer time(in minutes) required by the respective experts to develop the application programmes as follows:

Programmes
Programmers	A	B	C	D
I	120	100	80	90
II	80	90	110	70
III	110	140	120	100
IV	90	90	80	90

 

Ans 4.

Problem:

We are given a cost matrix (in minutes) representing the time each programmer takes to develop each program:

Programmers	A	B	C	D
I	120	100	80	90
II	80	90	110	70
III	110	140	120	100
IV	90	90	80	90

 

Step 1: Row Reduction

Subtract the minimum value in each row from every element in that row.

• Row I → Min = 80 → [40, 20, 0, 10]

 

 

 

Q5. Explain the economic interpretation of duality.

Ans 5.

Economic Interpretation of Duality in Linear Programming

Linear Programming

Duality is an essential concept in linear programming that connects every linear programming problem (called the primal) with another associated problem (called the dual). While the primal problem focuses on optimizing an objective function—such as maximizing profit or minimizing cost—the dual provides a complementary perspective that interprets the value of resources or constraints in the primal. Every constraint in the primal corresponds to a variable in the dual, and every variable in the primal corresponds to a constraint in the dual. This dual

 

 

Q6. Find out the optimal solution for the following transportation.

	D1	D2	D3	D4	Supply
S1	11	13	17	14	250
S2	16	18	14	10	300
S3	21	24	13	10	400
Demand	200	225	275	250

 

Ans 6.

To solve this transportation problem and find the optimal solution, we will use the following steps:

• Verify balance (supply = demand)
• Initial feasible solution using the Least Cost Method
• Optimality test using the MODI method (u-v method)

 

Step 1: Transportation Table Setup

Source → Destination ↓	D1	D2	D3	D4	Supply
S1	11	13	17	14	250