question_answer 25)

A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below :       Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs7.50 and that on each toy of type B is Rs.5, show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.  

Answer:

Let number of toys of type A = x       And number of toys of type B = y       The number of minutes to make one unit of toy of each type is given below :       The above L.P.P. is given as       Maximize Profit P = 7.50x P = 7.50x + 5y, subject to the constraints 12x + 6y , 18x , 6x + 9y       i.e. 2x + y       2x + 3y       L1 : 2x + y = 60                    L2 : 2x + 3y = 120         Z is maximum at E(15, 30) and maximum profit is Rs.262.50.