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Answer :

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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