Q26 of 45 Page 250

The corner points of the feasible region determined by the system of linear constraints are (0, 0), (0, 40), (20, 40), (60, 20), (60, 0). The objective function is Z = 4x + 3y.

Compare the quantity in Column A and Column B


A. The quantity in column A is greater


Z = 4x + 3y


Corner points- (0, 0), (0, 40), (20, 40), (60, 20), (60, 0)


As feasible region is bounded.


Value of Z at corner points-


At (0, 0), Z = 0


At (0, 40), Z = 120


At (20, 40), Z = 200


At (60, 20), Z = 360


At (60, 0), Z = 240


Clearly, maximum value of Z is 360, which is greater than 325.

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24

A company makes 3 model of calculators: A, B and C at factory I and factory II. The company has orders for at least 6400 calculators of model A, 4000 calculator of model B and 4800 calculator of model C. At factory I, 50 calculators of model A, 50 of model B and 30 of model C are made every day; at factory II, 40 calculators of model A, 20 of model B and 40 of model C are made every day. It costs Rs 12000 and Rs 15000 each day to operate factory I and II, respectively. Find the number of days each factory should operate to minimise the operating costs and still meet the demand.

 25

Maximise and Minimise Z = 3x – 4y

subject to x – 2y ≤ 0


– 3x + y ≤ 4


x – y ≤ 6


x, y ≥ 0

 27

The feasible solution for a LPP is shown in Fig. 12.12. Let Z = 3x – 4y be the


objective function. Minimum of Z occurs at

 28

Refer to Exercise 27. Maximum of Z occurs at