Question

A manufacturing company makes Iwo types of teaching aids A and B of Mathematics for class X11. Each type of A requires 9 labour hours of fabricating and 1 hour for finishing. Each type of B requires 12 labour hours for fabricating and 3 labour hours for finishing. For fabricating and finishing, the maximum labour hours available per week are 180 and 30 respectively. The company makes a profit of Rs.80 on each piece of type A and Rs.120 on each piece of type B. Flow many pieces of type A and type B should be manufactured per week to get a maximum profit?
Make it as an LPP and solve graphically. What is the maximum profit per week?

Answer 1

Let the number of pieces of type A and type B manufactured per week be x and y respectively. To maximize : Z = Rs. (80x + 120y)

Subject to constraints : $x\ge 0,y\ge 0$,

$9x+12\le 180\Rightarrow 3x+4y\le 60$,
$x+3y\le 30$

$\begin{array}{cc}\text{Corner points feasible region}& \text{Value of Z (in Rs.)}\\ O(0,0)& 0\\ A(0,10)& 1200\\ B(12,6)& 1680\\ C(20,0)& 1600\end{array}$

So, maximum profit of Rs. 1680 is obtained when 12 pieces of type A and 6 pieces of type B are manugactured by the company per week.