The maximum value of z = 3x + 5y subject to t | vedclass

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(B) The objective function is $z = 3x + 5y$.The constraints are $3x + 2y \leq 18$,$x \leq 4$,$y \leq 6$,and $x, y \geq 0$.The feasible region is a pol

Vedclass · Accepted Answer

$36$

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(B) The objective function is $z = 3x + 5y$.The constraints are $3x + 2y \leq 18$,$x \leq 4$,$y \leq 6$,and $x, y \geq 0$.The feasible region is a polygon with corner points $O(0, 0)$,$A(4, 0)$,$B(4, 3)$,$C(2, 6)$,and $D(0, 6)$.We evaluate $z$ at each corner point:At $O(0, 0)$: $z = 3(0) + 5(0) = 0$At $A(4, 0)$: $z = 3(4) + 5(0) = 12$At $B(4, 3)$: $z = 3(4) + 5(3) = 12 + 15 = 27$At $C(2, 6)$: $z = 3(2) + 5(6) = 6 + 30 = 36$At $D(0, 6)$: $z = 3(0) + 5(6) = 30$The maximum value of $z$ is $36$ at the point $(2, 6)$.

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

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