Question

A toy company manufactures two types of dolls,A and B.Market tests and available resources have indicate that the combined production lebel should not exceed 1200 dolls per week and the demand for dolls of type B is at most half of that for dolls of type A.Further the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600units.If the company makes profit of Rs12 and Rs16 per doll respectively on dolls A and B,how many of each should be produced weekly in order to maximize the profit?

Answer 1

Let x and y be the number of dolls of type A and B respectively that are produced per week.

The given problem can be formulated as follows.

Maximize
Z=12x+16y…………..(1)

Subject to the constraints,
x+y≤1200…………....(2)
y≤\frac{x}{2}$$\Rightarrowx≥2y………………..(3)
x-3y≤600....(4)
x,y≥0...(5)

The feasible region determined by the system of constraints is as follows.

The corner points are A(600,0),B(1050,150),and C(800,400).
The value of Z at these points are as follows.

Corner point| Z=12x+16y|
---|---|---
A(600,0)| 7200|
B(1050,150)| 15000|
C(800,400)| 16000| $\rightarrow$Maximum

The maximum value of Z is 16000 at(800,400).

Thus,800 and 400 dolls of type A and type B should be produced respectively to get the maximum profit of Rs16000.