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A company produces two types of cricket balls A and B. The production time of one ball of type B is double type A (time in units). The company has the time to produce a maximum of 2000 balls per day. The supply of raw materials is sufficient for the production of 1500 balls (both A and B) per day. The company wants to make maximum profit by making a profit of Rs. 3 from a ball of type A and Rs. 5 from type B.

Then, 

(i) By defining suitable variables write the objective function. 

(ii) Write the constraints. 

(iii) How many balls should be produced in each type per day in order to get maximum profit?

1 Answer

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(i) Let x be the number of balls of type A and y be the number of balls of type B. Then Maximise profit is Z = 3x + 5y 

(ii) Balls constraints 2x + y < 2000 investment constraint x + y < 1500 Therefore; Maximise; Z = 3x + 5y, 2x + y < 2000, x + y < 1500, x < 0, y < 0

(iii) In the figure the shaded region OABC is the fesible region. Here the region ¡s bounded. The corner points are O(0, 0), A(1000, 0) B(500, 1000), C(0, 1500). Given; Z = 3x + 5y

Corner points

Value of Z

O

Z = 3(0)+ 5(0) = 0

A

Z = 3(1000) + 5(0) = 3000

B

Z= 3(500) + 5(1000) = 6500

C

Z= 3(0) + 5(1500) = 7500

Since maximum value of Z occurs at C, the solution is

 Z = 3(0) + 5(1500) = 7500.

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