Answer to Question #203351 in Operations Research for Raghav Sood

Question

A manufacturer has two products P₁ and P₂ , both of which are produced in two steps by machines M₁ and M₂. The process time per hundred for the products on the machines

M₁ M₂ Profit(in

thousand Rs.

per 100 units)

P₁ 4 5 10

P₂ 5 2 5

Available 100 80

hours

The manufacturer can sell as much as he can produce of both products. Formulate the problem as LP model. Determine optimum solution, using simplex method.

Answer 1

Solution:

Let the number of required products $P_1, P_2$ be $x,y$ respectively.

Maximize, profit function, $P=10x+5y$

subject to constraints,

$x\ge0, y\ge0 \\ 4x+5y\le100 \\ 5x+2y\le80$

After introducing slack variables:

Max Z=10x+5y+0S₁+0S₂

subject to

5x+2y+S₁=80

4x+5y+S₂=100

and x,y,S₁,S₂≥0

Since all Z_j-C_j≥0

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

x=11.7647, y=10.5882

Max Z=170.5882