CASE STUDY CHALLENGE

Linear Programming: Factory Optimization

A factory manufactures tennis rackets and cricket bats.

  • • Tennis Racket: Takes 1.5 hours of machine time and 3 hours of craftsmanship.
  • • Cricket Bat: Takes 3 hours of machine time and 1 hour of craftsmanship.

In a day, the factory has availability of not more than 42 hours of machine time and 24 hours of craftsmanship.

Profit: ₹ 20 on a racket and ₹ 10 on a bat.

Based on the above information, answer the following questions:

Answer the following:

(i) If x and y are the numbers of bats and rackets manufactured by the factory, then write the expression of total profit. [1]
(ii) Write the constraint that relates the number of craftsmanship hours. [1]
(iii) (a) Determine the maximum profit (in ₹) earned by the factory.

— OR —

(b) How many bats and rackets respectively, are to be manufactured to earn maximum profit?

 [2]
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