A toy company manufactures two types of dolls, A and B. Market tests and available resources have indicated that the combined production level 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 600 units. If the company makes profit of Rs 12 and Rs 16 per doll respectively on dolls A and B, how many of each should be produced weekly in order to maximise the profit?
Verified Answer
Let ‘x’ and ‘y’ be the number of dolls produced/week of type A and B respectively.
Maximize: = 12x + 16yz
S.t. x + y 1200
y ≤ x/2
x - 3y ≤ 60
x, y ≥ 0
The feasible region is OABC Z = 12x + 16y
O (0, 0) 0
A (600, 0) 7200
B (1050, 150) 15, 000
C (800, 400) 16, 000
Maximum value is Rs 16, 000 at (800, 400) so 800 dolls of type A and 400 of type B, should be made to maximize the profit.