question_answer 1)

A company manufactures two types of novelty souvenirs made of plywood. Souvenirs of type A required 5 minutes each for cutting and 10 minutes each for assembling. There are 3 hours 20 minutes available for cutting and 4 hours for assembling. Souvenirs of type B require 8 minutes each for cutting and 8 minutes each fror assembling. The profit is Rs.5 each for type A and Rs.6 each for type B souvenirs How many souvenirs of each type should the company manufacture in order to maximize the profit ? 

Answer:

Let number of souvenirs of type A = x         and number of sonvenirs of type B = y       The number of minutes for manufacturing 1 unit of souvenirs of each type is given below :             Therefore the above L.P.P. is given as       Maximize, P = 5x + 6y, subject to the constraints 5x + 8y  10x + 8y  x, y       L1 : 5x + 8y = 200                L2 : 10x + 8y = 240                                         Here P is maximum at E (8, 20)        For maximum profit        Number of souvenirs of type A = 8       Number of souvenirs of type B = 20.