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4.A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftman’s time in its making while a cricket bat takes 3 hour of machine time and 1 hour of craftman’s time. In a day, the factory has the availability of not more than 42 hours of machine time and 24 hours of craftsman’s time.
(ii) If the profit on a racket and on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity.
Answers (1)
Let the number of rackets is x and the number of bats is y.
the machine time availability is not more than 42 hours.
craftsman’s time availability is 24 hours
The given information can be repreented in table as shown :
| racket | bat | availability | |
| machine time | 1.5 | 3 | 42 |
| craftman's time | 3 | 1 | 24 |
The profit on the bat is 10 and on the racket is 20.
The mathematical formulation is :
maximise
subject to constraints,
The feasible region determined by constraints is as follows:
The corner points are
The value of Z at corner points is as shown :
| CORNER POINTS | ||
| 160 | ||
| 200 | maximum | |
| 140 | ||
| 0 |
Thus, the maximum profit of the factory when it works at full capacity is 200.
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