The maximum value of Z=x+y,subjected to x+y l | vedclass

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(C) The feasible region is bounded by the lines $x+y=10$,$5x+3y=15$,$x=6$,and the axes $x=0, y=0$.The corner points of the feasible region are $A(0, 5

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occurs at infinitely many points

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(C) The feasible region is bounded by the lines $x+y=10$,$5x+3y=15$,$x=6$,and the axes $x=0, y=0$.The corner points of the feasible region are $A(0, 5)$,$B(0, 10)$,$C(6, 4)$,$D(6, 0)$,and $E(3, 0)$.We evaluate the objective function $Z=x+y$ at each corner point:At $A(0, 5)$,$Z = 0 + 5 = 5$.At $B(0, 10)$,$Z = 0 + 10 = 10$.At $C(6, 4)$,$Z = 6 + 4 = 10$.At $D(6, 0)$,$Z = 6 + 0 = 6$.At $E(3, 0)$,$Z = 3 + 0 = 3$.The maximum value of $Z$ is $10$,which occurs at both points $B(0, 10)$ and $C(6, 4)$.Since the objective function attains the same maximum value at two distinct corner points,it attains the same maximum value at every point on the line segment joining these two points.Therefore,the maximum value of $Z$ occurs at infinitely many points.

The maximum value of $Z=x+y$,subjected to $x+y \leq 10$,$5x+3y \geq 15$,$x \leq 6$,$x, y \geq 0$.

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