Answer to Question #226210 in Operations Research for mafi

Question

1.     A company produces two types of products say type A and type B. Product A is of superior quality and product B is of a lower quality. Respective profits for the two types of products are BIRR 40 and BIRR 30.

The data on the resource required, availability of resources are given below:

 

Requirement

Capacity available per month

Product A

Product B

Raw materials (kg)

120

60

12000

Machining time (hrs/piece)

5

8

600

Assembly (man-hour)

4

3

500

Required:

                i.           Formulate the problem as LPP?

              ii.           Solve using Simplex method.

Answer 1

Solution:

Let the units of Type A and Type B produced respectively be $x,\ y$ .

(i): Maximise $Z = 40x+30y$ subject to the constraints:

$120x+60y\le12000 \\ 5x+8y\le600 \\ 4x+3y\le500 \\ x,y\ge 0$

(ii):

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

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 should add slack variable S3

After introducing slack variables

Since all Zj-Cj≥0

Hence, the optimal solution is arrived with the value of variables as :

x=90.9091,y=18.1818

Max Z=4181.8182