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(B) To find the minimum value of the objective function $z = 3x + 2y$,we evaluate $z$ at each corner point of the feasible region:$1$. At point $A(3,

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$15$

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(B) To find the minimum value of the objective function $z = 3x + 2y$,we evaluate $z$ at each corner point of the feasible region:$1$. At point $A(3, 3)$: $z = 3(3) + 2(3) = 9 + 6 = 15$$2$. At point $B(20, 3)$: $z = 3(20) + 2(3) = 60 + 6 = 66$$3$. At point $C(20, 10)$: $z = 3(20) + 2(10) = 60 + 20 = 80$$4$. At point $D(18, 12)$: $z = 3(18) + 2(12) = 54 + 24 = 78$$5$. At point $E(12, 12)$: $z = 3(12) + 2(12) = 36 + 24 = 60$Comparing these values,the minimum value of $z$ is $15$.

For a Linear Programming $(LP)$ problem,the objective function is $z = 3x + 2y$. The coordinates of the corner points of the bounded feasible region are $A(3, 3)$,$B(20, 3)$,$C(20, 10)$,$D(18, 12)$,and $E(12, 12)$. The minimum value of $z$ is . . . . . . .

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