The objective function z=x_1+x_2,subject to x | vedclass

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(C) The feasible region is determined by the constraints $x_1+x_2 \leq 10$,$-2x_1+3x_2 \leq 15$,$x_1 \leq 6$,and $x_1, x_2 \geq 0$. The corner points

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at every point of the segment joining two points

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(C) The feasible region is determined by the constraints $x_1+x_2 \leq 10$,$-2x_1+3x_2 \leq 15$,$x_1 \leq 6$,and $x_1, x_2 \geq 0$. The corner points of the feasible region are $O(0,0)$,$E(6,0)$,$F(6,4)$,$G(3,7)$,and $D(0,5)$.We evaluate the objective function $z=x_1+x_2$ at these corner points:$z(O) = 0+0 = 0$$z(E) = 6+0 = 6$$z(F) = 6+4 = 10$$z(G) = 3+7 = 10$$z(D) = 0+5 = 5$The maximum value of $z$ is $10$,which occurs at both corner points $F(6,4)$ and $G(3,7)$.Since the objective function is maximized at two distinct corner points,it will have the same maximum value at every point on the line segment joining these two points.

The objective function $z=x_1+x_2$,subject to $x_1+x_2 \leq 10, -2x_1+3x_2 \leq 15, x_1 \leq 6, x_1, x_2 \geq 0$,has a maximum value at:

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