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Misc 4 - A manufacturer makes two types of toys A and B.

Misc 4 - Chapter 12 Class 12 Linear Programming - Part 2
Misc 4 - Chapter 12 Class 12 Linear Programming - Part 3
Misc 4 - Chapter 12 Class 12 Linear Programming - Part 4
Misc 4 - Chapter 12 Class 12 Linear Programming - Part 5
Misc 4 - Chapter 12 Class 12 Linear Programming - Part 6

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Misc 4 A manufacturer makes two types of toys A and B. Three machines are needed for this purpose and the time (in minutes) required for each toy on the machines is given below: Each machine is available for a maximum of 6 hours per day. If the profit on each toy of type A is Rs 7.50 and that on each toy of type B is Rs 5, show that 15 toys of type A and 30 of type B should be manufactured in a day to get maximum profit.Let number of toys of type A be x, number of toys of type B be Y According to Question According to Question Machine II Time required on Type A → 18 Min Type B → 0 Min Max Available Time = 360 min ∴ 18x + 0.y ≤ 360 x ≤ 20 Machine III Time required on Type A → 6 Min Type B → 9 Min Max Available Time = 360 min ∴ 6x + 9y ≤ 360 2x + 3y ≤ 120 As we need to maximize the Profit Profit on Type A → Rs 7.50 Profit on Type B → Rs 5 ∴ Z = 7.50 x + 5y Combining all constraints : Max Z = 7.5x + 5y Subject to constraints, 2x + y ≤ 60, x ≤ 20, 2x + 3y ≤ 120, & x ≥ 0 , y ≥ 0 Hence, profit will be maximum if Number of Type A toys = 15 Number of Type B toys = 30 Maximum Profit = Rs. 262.50 Hence, profit will be maximum if Number of Type A toys = 15 Number of Type B toys = 30 Maximum Profit = Rs. 262.50

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.