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(D) To find the maximum and minimum values of the objective function $z = 3x - 4y$,we evaluate $z$ at each corner point of the feasible region shown i

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$-17$

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(D) To find the maximum and minimum values of the objective function $z = 3x - 4y$,we evaluate $z$ at each corner point of the feasible region shown in the figure:Corner Point $(x, y)$Objective Function $z = 3x - 4y$$(0, 0)$$z = 3(0) - 4(0) = 0$$(5, 0)$$z = 3(5) - 4(0) = 15$ (Maximum value)$(6, 5)$$z = 3(6) - 4(5) = 18 - 20 = -2$$(6, 8)$$z = 3(6) - 4(8) = 18 - 32 = -14$$(4, 10)$$z = 3(4) - 4(10) = 12 - 40 = -28$$(0, 8)$$z = 3(0) - 4(8) = -32$ (Minimum value)From the table,the maximum value of $z$ is $15$ and the minimum value of $z$ is $-32$.Therefore,(Maximum value of $z$) + (Minimum value of $z$) $= 15 + (-32) = 15 - 32 = -17$.

The feasible solution for a Linear Programming Problem $(LPP)$ is shown in the figure. Let $z = 3x - 4y$ be the objective function. The value of (Maximum value of $z$ + Minimum value of $z$) is equal to $....$

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