Question 28

A manufacturer makes two types of toys A and B. Three machine are needed for this purpose and the time (in minutes) required for each toy on the machines is given below:

Types of Toys

Machines

I

II

III

A

20

10

10

B

10

20

30

The machines I, II and III are available for a maximum of 3 hours, 2 hours and 2 hours 30 minutes respectively. The profit on each toy of type A is Rs 50 and that of type B is Rs 60. Formulate the above problem as a L.P.P and solve it graphically to maximize profit.

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Question 28 A manufacturer makes two types of toys A and B. Three machine are needed for this purpose and the time (in minutes) required for each toy on the machines is given below: The machines I, II and III are available for a maximum of 3 hours, 2 hours and 2 hours 30 minutes respectively. The profit on each toy of type A is Rs 50 and that of type B is Rs 60. Formulate the above problem as a L.P.P and solve it graphically to maximize profit. Let Number of toys of Type A be x, Number of toys of Type B be y Given that The profit on each toy of type A is Rs 50 and that of type B is Rs 60 We need to maximize the Profit ∴ Z = 50x + 60y Now, according to question Max time available on Machine I = 3 hours = 180 minutes Max time available on Machine II = 2 hours = 120 minutes Max time available on Machine III = 2.5 hours = 150 minutes Machine I Max Time = 180 mins ∴ 20x + 10 y ≤ 180 2x + y ≤ 18 Machine II Max Time = 120 mins ∴ 10x + 20y ≤ 120 x + 2y ≤ 12 Machine III Max Time = 150 mins ∴ 10x + 30 y ≤ 150 x + 3y ≤ 15 Machine III Max Time = 150 mins ∴ 10x + 30 y ≤ 150 x + 3y ≤ 15 Combining all constraints : Max Z = 50x + 60y Subject to constraints, 2x + y ≤ 18, x + 2y ≤ 12 x + 3y ≤ 15 & x ≥ 0 , y ≥ 0 2x + y ≤ 18 x + 2y ≤ 12 x + 3y ≤ 15 2x + y ≤ 18 x + 2y ≤ 12 x + 3y ≤ 15 Hence, profit will be maximum if Number of toys of Type A = 8 Number of toys of Type B = 2 Maximum Profit = Rs. 520

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.