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Manufacturing problems

Example 8
Deleted for CBSE Board 2023 Exams

Ex 12.2, 3 Important Deleted for CBSE Board 2023 Exams You are here

Ex 12.2, 4 Important Deleted for CBSE Board 2023 Exams

Ex 12.2, 5 Deleted for CBSE Board 2023 Exams

Ex 12.2, 6 Deleted for CBSE Board 2023 Exams

Ex 12.2, 7 Important Deleted for CBSE Board 2023 Exams

Misc 4 Important Deleted for CBSE Board 2023 Exams

Misc 10 Important Deleted for CBSE Board 2023 Exams

Example 10 Deleted for CBSE Board 2023 Exams

Last updated at Feb. 17, 2020 by Teachoo

Ex 12.2, 3 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 & 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 & on a bat is Rs 20 and Rs 10 respectively, find the maximum profit of the factory when it works at full capacity.Let Number of Tennis Racket be x Number of Cricket Bats be y According to Question : As we want Maximize the profit. Hence the function used here will be Maximize Z Machine Hours Tennis Racket requires → 1.5 hrs Cricket Bat requires → 3 hrs Max time available → 42 hrs ∴ 1.5x + 3y ≤ 42 3x + 6y ≤ 84 x + 2y ≤ 28 Craftsman's Hours Tennis Racket requires → 3 hrs Cricket Bat requires → 1 hrs Max time Available → 24 hrs ∴ 3x + y ≤ 24 Profit on each tennis racket → Rs 20 Profit on each Cricket Bat → Rs 10 ∴ Max Z = 20x + 10y Combining all the constraints : Maximize Z = 20x + 10y Subject to constraints, x + 2y ≤ 28 3x + y ≤ 24 x ≥ 0, y ≥ 0 x + 2y ≤ 28 3x + y ≤ 24 Thus, 4 Tennis Rackets and 12 Cricket Bats must be made so that factory runs at full capacity. Maximum Profit is Rs 200, when 4 tennis bats and 2 cricket bats are Produced.