The maximum value of Z=3x+5y,subject to the c | vedclass

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(C) The feasible region is determined by the constraints $3x+2y \leq 18$,$x \leq 4$,$y \leq 6$,and $x, y \geq 0$. The vertices of the feasible region

Vedclass · Accepted Answer

$36$

Vedclass · Answer

(C) The feasible region is determined by the constraints $3x+2y \leq 18$,$x \leq 4$,$y \leq 6$,and $x, y \geq 0$. The vertices of the feasible region are $O(0,0)$,$D(4,0)$,$Q(4,3)$,$P(2,6)$,and $C(0,6)$.We evaluate the objective function $Z=3x+5y$ at each vertex:At $O(0,0)$: $Z = 3(0) + 5(0) = 0$At $D(4,0)$: $Z = 3(4) + 5(0) = 12$At $Q(4,3)$: $Z = 3(4) + 5(3) = 12 + 15 = 27$At $P(2,6)$: $Z = 3(2) + 5(6) = 6 + 30 = 36$At $C(0,6)$: $Z = 3(0) + 5(6) = 30$Comparing these values,the maximum value of $Z$ is $36$ at the point $(2,6)$.

The maximum value of $Z=3x+5y$,subject to the constraints $3x+2y \leq 18$,$x \leq 4$,$y \leq 6$,and $x, y \geq 0$ is

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