question_answer 15)

A factory manufactures two types of services. A and B; each type requiring the use of two machines an automatic and a hand operated. It takes 4 minutes on the automatic and 6 minutes on hand operated machines to manufacture a package of screws A, while it takes 6 minutes on automatic and 3 minutes on the hand operated machines to manufacture a package of screws B. Each machine is available for at the most 4 hours on any day. The manufacturer can sell a package of screws A at a profit of Rs.7 and screws B at a profit of Rs.10. Assuming that he can sell all the screws he manufactures, how many packages of each type should the factory owner produce in a day in order to maximize his profit Determine the maximum profit.  

Answer:

Let number of packages of screws A produced = x              and number of packages of screws B produced = y       The number of minutes for producing 1 unit of each item is given below.             Therefore, the above L.P.P. is given as       Maximize, P = 7x + 10y subject to the constaints.             4x + 6y  240; 6x + 3y  240       i.e. 2x + 3y  120; 2x + y  80, x, y 0       L1 : 2x + 3y + 120    L2 : 2x + y + 80                          Here profit is maximum at E (30, 20)        Number of packages of screws A = 30       Number of packages of screws B = 20       Maximum profit = Rs.410