question_answer 14)

A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 horus on machine B to produce a package of nuts while it takes 3 hours on machine A and 1 hours on machine B to produce a package of bolts. He earns a profit of Rs.17.50 per package on nuts and Rs.7.00 per package on bolts. How may packages of each should be produced each day so as to maximize his profit, it he operates his machines for at the most 12 hours a day ? 

Answer:

Let number of packages of nuts produced = x       and number of packages of bolds produced = y       The number of hours for producing 1 unit of each item is given below :             Therefore the above LPP is given as       Maximize, P = 17.50 x + 7y, subject to constrains       x + 3y       L1 : x + 3y = 12                    L2 : 3x + y = 12              Here P is maximum at E (3, 3)        Number of Nuts = 3       Number of Bolts = 3