Question

A manufacturing company makes two models A and B of a product. Each piece of model A requires 9 hours of labour for fabricating and 1 hour for finishing. The maximum number of labour hours, available for fabricating and for finishing are 180 and 30 respectively. The company makes a profit of Rs. 8000 and Rs. 12000 on each piece of model A and B respectively. How many pieces of each model should be manufactured to get maximum profit ? Also, find the maximum profit.

Answer 1

Let the number of pieces of model A and model B respectively be x and y.
To maximize : Z = Rs (8000x + 12000y)
Subject to the constraints : $9x+12y\le 180,x+3y\le 30,x\ge 0,y\ge 0$
that is, $3x+4y\le 60,x+3y\le 30,x\ge 0,y\ge 0$
$\begin{array}{cc}\text{Corner points}& \text{Value of Z(in Rs.)}\\ \text{O(0,0)}& \text{0}\\ \text{C(20,0)}& \text{160000}\\ \text{B(12,6)}& \text{168000}\\ \text{A(0,10)}& \text{120000}\end{array}$
The number of pieces of model A and model B are 12 and 6 respectively.
Also maximum profit is of Rs. 168000.