The feasible region of a linear programming ...

CBSE Class 12 Math 2026 All Sets Solved Paper

Question : 17 of 20

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The feasible region of a linear programming problem with objective function Z = 5x + 7 y is shown below :

The maximum value of Z – minimum value of Z is

Solution:

The corner points of the bounded feasible region are (0, 0), (7, 0), (3, 4), (0, 2)

Now,

Z=5 x+7 y

At (0, 0) ; Z = 5(0) + 7(0) = 0

At (7, 0) ; Z = 5(7) + 7(0) = 35

At (3, 4) ; Z = 5(3) + 7(4) = 43

At (0, 2) ; Z = 5(0) + 7(2) = 14

∴ Z_{max}=43

(at point (3,4))

Z_{min}=0

(at point (0, 0))

∴ Z_{max}-Z_{min}=43-0=43

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