A manufacture produces nuts and bolts for industrial machinery. It takes 1 hour of work on machine A and 3 hours on machine B to produces a packet of nuts while it takes 3 hours on machine A and 1 hours on machine B to produce a packet of bolts. He earns a profit ₹17.50 per packet on nuts and ₹7 per packet on bolts. How many packets of each should be produced each day so as to maximize his profit if he operates each machine for at the most 12 hours a day? Also find the maximum profit.


Let the number of packets of nuts and bolts be x and y respectively.


∴According to the question,


X + 3y


Maximize Z = 17.50x + 7y


The feasible region determined by X + 3y is given by



The corner points of the feasible region are A(0,0), B(0,4), C(3,3)), D(4,0).The value of Z at the corner point is



The maximum value of Z is 73.50 at (3,3).


The manufacturer should make 3 packets each of nuts and bolts to make maximum profit of Rs.73.50.


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