Explain why in LPP only corner points give us maximum and minimum values and not any other point in the feasible region

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Solution

Dear Student,

In any LPP the optimum function is maximum or minimum only at the corner points as, in the feasible region consider in along any straight line either the function increases or decreases along any straight line between 2 corner points, either the function value increases or decreases till another corner point is reached. Hence maximum or minimum values occur only at corner points of feasible region.

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(0, 2),

(3, 0),

(6, 0),

(6, 8)

and

(0, 5) .

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Z = 4 x + 6 y

be the objective function. Then minimum value of

Z

occurs at

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