The maximum value of Z = 3x + 4y subject to t | vedclass

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(A) To find the maximum value of $Z = 3x + 4y$ subject to the constraints $x + y \leq 4, x \geq 0, y \geq 0$,we identify the corner points of the feas

Vedclass · Accepted Answer

$16$

Vedclass · Answer

(A) To find the maximum value of $Z = 3x + 4y$ subject to the constraints $x + y \leq 4, x \geq 0, y \geq 0$,we identify the corner points of the feasible region.The feasible region is a triangle with vertices at $(0, 0)$,$(4, 0)$,and $(0, 4)$.Now,we evaluate $Z$ at each corner point:$1$. At $(0, 0)$: $Z = 3(0) + 4(0) = 0$$2$. At $(4, 0)$: $Z = 3(4) + 4(0) = 12$$3$. At $(0, 4)$: $Z = 3(0) + 4(4) = 16$Comparing these values,the maximum value of $Z$ is $16$ at the point $(0, 4)$.Therefore,the correct option is $A$.

The maximum value of $Z = 3x + 4y$ subject to the constraints $x + y \leq 4, x \geq 0, y \geq 0$ is . . . . . . .

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