Question

A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time(in minutes)required for each toy on the machines is given below:

Each machine is available for a maximum 6 hours per day.If the profit on each toy of type A is Rs7.50 and that on each toy of type B is Rs5, show that 15 toys of type A and 30 toys of type B should be manufactured in a day to get maximum profit.

Answer 1

Let X and Y toys of type A and type B respectively manufactured in a day.

The given problem can be formulated as follows.

Maximize Z=7.5x+5y..(1)

Subject to the constraints,
2x+y≤60...(2)
x≤20...(3)
2x+3y≤120....(4)
x,y≥0...(5)

The feasible region determined by the constraints is as follows.

The corner points of the feasible region are A(20,0), B(20,20), C(15,30) and D(0,40).

The value of Z at these corner points is as follows.

Corner point| Z=7.5x+5y|
---|---|---
A(20,0)| 150|
B(20,20)| 250|
C(15,30)| 262.5| $\rightarrow$Maximum
O(40,0)| 200|

Thus, the manufacturer should manufacture 15 toys of type A and 30 types of toy B to maximize the profit.