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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. 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?
  • a)
    Maximum profit = Rs 220
  • b)
    Maximum profit = Rs 210
  • c)
    Maximum profit = Rs 200
  • d)
    Maximum profit = Rs 230
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
A factory makes tennis rackets and cricket bats. A tennis racket takes...
Let number of rackets made = x 
And number of bats made = y 
Therefore , the above L.P.P. is given as : 
Maximise , Z = x +y , subject to the constraints : 1.5x +3y ≤ 42 and. 3x +y ≤ 24, i.e.0.5x + y ≤ 14 i.e. x +2y ≤ 28 and 3x +y ≤ 24 , x, y ≥ 0.

Here Z = 16 is maximum. i.e Maximum number of rackets = 4 and number of bats = 12.
Here , profit function is P = 20x + 10y 
Profit is maximum at x = 4 and y = 12 . 
Therefore , maximum profit = 20(4) + 10 ( 12) = 200.i.e. Rs.200.
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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. 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?a)Maximum profit = Rs 220b)Maximum profit = Rs 210c)Maximum profit = Rs 200d)Maximum profit = Rs 230Correct answer is option 'C'. Can you explain this answer?
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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. 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?a)Maximum profit = Rs 220b)Maximum profit = Rs 210c)Maximum profit = Rs 200d)Maximum profit = Rs 230Correct answer is option 'C'. Can you explain this answer? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about 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. 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?a)Maximum profit = Rs 220b)Maximum profit = Rs 210c)Maximum profit = Rs 200d)Maximum profit = Rs 230Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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. 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?a)Maximum profit = Rs 220b)Maximum profit = Rs 210c)Maximum profit = Rs 200d)Maximum profit = Rs 230Correct answer is option 'C'. Can you explain this answer?.
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