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Ex 12.2, 4 - A manufacturer produces nuts and bolts. - Manufacturing problems

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  1. Class 12
  2. Important Question for exams Class 12
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Ex 12.2, 4 A manufacturer produces nuts and bolts. It takes 1 hour of work on machine A and 3 hours on machine B to produce a package of nuts. It takes 3 hours on machine A and 1 hour on machine B to produce a package of bolts. He earns a profit of Rs 17.50 per package on nuts and Rs 7.00 per package on bolts. Ho many packages of each should be produced each day so as to maximise his profit, if he operates his machines for at the most 12 hours a day? Let number of packages of nuts produced be x number of packages of bolts produced be y According to Question : As we need to Maximize the profit, the function used here will be Maximize Z. Profit on each Nut → Rs 17.50 Profit on each bolt → Rs 7.50 ∴ Maximize Z = 17.5 x + 7.5y Combining all constraints : Maximize Z = 17.5x + 7.5y Subject to constraints : x + 3y ≤ 12 3x + y ≤ 12 x ≥ 0, y ≥ 0 Hence, the Profit will be maximum if the Company produces : Number of bolts → 3 packages Number of nuts → 3 packages Maximum Profit = Rs 73.50

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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