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The optimal solution based on the constraints and objective function is as follows:

1. **Number of tennis rackets to produce**: 4
2. **Number of cricket bats to produce**: 12
3. **Maximum profit**: Rs 200

This solution ensures the factory operates at full capacity while maximizing profit.

Let me know if you want more details or have any questions.

Here are 5 related questions:
1. How would the solution change if the available machine time was reduced to 36 hours?
2. What happens to the profit if the craftsman's time is increased by 6 hours?
3. Can the factory make only tennis rackets and still meet its constraints?
4. How would a change in profit per bat (e.g., Rs 15) affect the optimal solution?
5. Can there be a situation where it's better to produce more bats than rackets for higher profit?

**Tip:** Always try to maximize profit by ensuring that both resources (machine time and craftsman's time) are used as efficiently as possible.

A factory makes tennis rackets and cricket bats. A tennis racket takes 1.5 hours of machine time and 3 hours of craftsman's time in its making while a cricket bat takes 3 hours of machine time and 1 hour of craftsman'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.
(i) What number of rackets and bats must be made if the factory is to work at full capacity?
(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.

Learn how to maximize the profit in a factory that produces tennis rackets and cricket bats. The factory has machine time and craftsman's time constraints. We use linear programming to find the optimal number of rackets and bats to produce while working at full capacity. Suitable for Grades 11-12.

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