Question

Question: A factory manufactures shoes and slipper. It takes 1 hour of labour work on machine A and 3 hours on machine B to produce a shoe. It takes 3 hours of
machine A and 1 hour on machine B to produce a slipper. A profit of Rs.20 per shoe and Rs 10 per slipper is earned. How many of each must be produced per
day so as to maximize the profit, if machines can be operated for maximum 12 hours per day?

Answer 1

Let denote the number of shoes and denote the number of slippers.

The our objective is to maximize

With constraints

Machine A

Machine B

Plot the constrants we get the feasible region as shown below

The cornor points of the region are (4,0) , (3,3) and (0,4)

The maximum value of the objective function is at (3,3)

Hence the factory should manufacture 3 shoes and 3 slippers each day to get a profit of