A toy company manufactures two types of dolls A and B. Resources indicate that the combined production level should not exceed 1200 dolls per week and the demand for dolls of type B is atmost 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 of atleast 600 units. If the company makes profit of Rs 12 and Rs 16 per doll respectively on dolls A and B. How many each should be produced weekly in order to maximize profit?

Asked by Topperlearning User | 31st Jul, 2016, 08:05: PM

Expert Answer:

Let the company manufactures x dolls of type A and y dolls of type B.
          We have the following LPP
          Maximum z = 12x + 16y
          y  x divided by 2 or x - 2y  0
          x - 3y  600
          x  0, y  0
         

Corner Points

Z = 12x + 16y

O(0, 0)
A(600, 0)
B(1050, 150)
C(800, 400)

z = 0
z = 7200
z = 15000
z = 16000

Hence, maximum profit is Rs 16000 when 800 dolls of type A and 400 dolls of type B are sold.

Answered by  | 31st Jul, 2016, 10:05: PM