The coordinates of the point for minimum value of Z = 7x – 8y subject to the conditions x + y ≤ 20, y ≥ 5, x ≥ 0, y ≥ 0 are ___________.

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Solution

For z = 7x − 8y

s.t x + y ≤ 20

y ≥ 5, x, y ≥ 0

The equality constraints corresponding to given constraints are x + y = 20, y = 5, x = 0, y = 0

Feasible region given by ABC

Points Value of z = 7x − 8y

A(0, 5) z = 7(0) − 8(5) = −40

B(0, 20) z = 7(0) − 8(20) = −160

C(15, 5) z = 7(15) − 8(5) = 65

Since minimum value is −160
∴ Coordinates for minimum value of z are (0, 20)

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