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A manufacturer produces nuts and bolts, It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of 17.50 per package of nuts and 7.00 per package of bolts. How many packages of each should be produced each day so as to maximise his profit, if he operates his machine for at most 12 hours a day ? Form the above as a linear programming problem and solve it graphically.

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Let x packages of nuts and y packages of bolts be produced each day.

Vertices of feasible region are 4(0,4) , B(3,3), C(4,0). Profit is maximum at B(3,3) i.e.,  3 packages of nuts and 3 packages of bolts

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