DOMS304 MBA APPLICATIONS OF OPERATIONS RESEARCH

Description

SESSION	JUL – AUG 2024
PROGRAM	MASTER OF BUSINESS ADMINISTRATION (MBA)
SEMESTER	3
COURSE CODE & NAME	DOMS304 APPLICATIONS OF OPERATIONS RESEARCH

 

 

Assignment Set – 1

 

1. A factory manufactures two products A and B. To manufacture one unit of A, 10 machine hours and 15 labour hours are required. To manufacture product B, 20 machine hours and 15 labour hours are required. In a month, 400 machine hours and 300 labour hours are available. Profit per unit for A is Rs. 75 and for B is Rs. 50. Formulate as LPP.

Ans 1.

Formulating the Linear Programming Problem (LPP)

In this scenario, a factory manufactures two products, A and B, using limited resources: machine hours and labor hours. The aim is to determine the optimal production quantities of these products to maximize profit while staying within the resource constraints. This problem can be formulated as a Linear Programming Problem (LPP) as follows:

Decision Variables

To represent the quantities of the two products, we define:

• : Number of units of product A to be produced.
• : Number of units of

 

 

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2. Find solution using Simplex method

MAX Z = 3×1 + 5×2 + 4×3

subject to

2×1 + 3×2 <= 8

2×2 + 5×3 <= 10

3×1 + 2×2 + 4×3 <= 15

and x1,x2,x3 >= 0

Ans 2.

Problem is

Max Z = 3 x1 + 5 x2 + 4 x3

subject to

2 x1 + 3 x2 ≤ 8 2 x2 + 5 x3 ≤ 10 3 x1 + 2 x2 + 4 x3 ≤ 15

and x1,x2,x3≥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
3. As the constraint-3 is of type ‘≤’ we

 

3. Solve the following LPP graphically

Max Z = 4x + 5y

Subject to

x + y ≤ 20

3x + 4y ≤ 72

x, y ≥ 0

 

Ans 3.
Problem is

MAX Z = 4 x1 + 5 x2

subject to

x1 + x2 ≤ 20 3 x1 + 4 x2 ≤ 72

 

 

 

 

 

Assignment Set – 2

 

4. Obtain an optimum solution to the following transportation problem

Factory	Warehouse				Capacity
	W1	W2	W3	W4
F1	19	30	50	10	7
F2	70	30	40	60	9
F3	40	8	70	20	18
Requirements	5	8	7	14

 

Ans 4.

Step-by-Step Solution to the Transportation Problem

Problem Data:

Factory	Warehouse W1	Warehouse W2	Warehouse W3	Warehouse W4	Capacity
F1	19	30	50	10	7
F2	70	30	40	60	9
F3	40	8	70	20	18

 

 

5. Consider the problem of assigning five jobs to five persons. The assignment costs are given as follows. Determine the optimum assignment schedule.

Job
Person	1	2	3	4	5
A	8	4	2	6	1
B	0	9	5	5	4
C	3	8	9	2	6
D	4	3	1	0	3
E	9	5	8	9	5

 

Ans 5.

Problem: Assignment of Jobs to Persons

The task involves assigning five jobs to five persons such that the total assignment cost is minimized. The cost matrix is given as:

	Job 1	Job 2	Job 3	Job 4	Job 5
A	8	4	2	6	1
B	0	9	5	5	4
C	3	8	9	2	6

 

 

6. Discuss the applications of Integer programming.

Ans 6.

Applications of Integer Programming

Integer Programming (IP) is a specialized field within optimization that focuses on problems requiring decision variables to take integer values. It is widely applied in various industries and sectors due to its ability to address real-world problems where solutions must be discrete, such as scheduling, allocation, and resource optimization. Below are key applications of Integer Programming,