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# A factory makes t

Let the number of rackets and the number of bats to be made be x and y respectively.

The machine time available is not more than 42 hours.

1.5x +3y ≤ 42

The craftsman`s time is not available for more than 24 hours

3x + y ≤ 24

The factory is to work at full capacity

1.5x + 3y = 42

3x + y = 24

Where x and y ≥ 0

Solving the two equations we get x= 4 and y = 12

Thus 4 rackets and 12 bats must be made

(i) The given information can be complied in the tables form as follows

The profit on a racket is Rs 20 and on bat is Rs 10

Maximize, Z = 20x +10y ………………1

Subject to constraints

1.5x + 3y = 42

3x + y = 24

x, y ≥ 0

the feasible region determined by the system of constraints is:

The corner points are A(8,0) , B(4, 12) , C(0, 14) and O(0,0)

The values of Z at these corner points are as follows:

Thus the maximum profit of the factory is when it works to its full capacity is Rs200.

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