A factory manufactures tennis rackets and cricket bats. A tennis racket takes 1 1/2 hours of machine time and 3 hours of craftsmanship in its making;…

A factory manufactures tennis rackets and cricket bats. A tennis racket takes $\displaystyle 1 \frac{1}{2}$ hours of machine time and $\displaystyle 3$ hours of craftsmanship in its making; while a cricket bat takes $\displaystyle 3$ hours of machine time and $\displaystyle 1$ hour of craftsmanship. In a day, the factory has availability of not more than $\displaystyle 42$ hours of machine time and $\displaystyle 24$ hours of craftsmanship. Profit on a racket and on a bat are ₹ $\displaystyle 20$ and ₹ $\displaystyle 10$ respectively.

Based on the above information, answer the following questions :

If x and y are the numbers of bats and rackets manufactured by the factory, then write the expression of total profit.

Write the constraint that relates the number of craftsmanship hours.