question_answer 30)

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 dols A and B, how many of each should be produced weekly in order to maximize the profit ? 

Answer:

Let the number of dols of type A manufactured = x       and the number of dolls of type B manufactured = y       Given that combined production level should not exceed 1200 dolls per week             The demand for dolls of type B is atmost half of that for dolls of type A             Also the production level of dolls of type A can exceed three times the production of dolls of other type by at most 600 units.                    Above L.P.P. is given as       Maximize, Z = 12x + 16y subject to the constraints, x + y             L1 : x + y = 1200            L2 : x ? 2y = 0       Here Z is maximum at (800, 400)       800 of type A and 400 dolls of type B should be produce to get maximum profit.