The minimum value of Z = 2x + 3y for the syst | vedclass

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(A) To find the minimum value of $Z = 2x + 3y$,we identify the feasible region defined by the constraints:$1$. $2x + 4y \leq 12 \implies x + 2y \leq 6

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$0$

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(A) To find the minimum value of $Z = 2x + 3y$,we identify the feasible region defined by the constraints:$1$. $2x + 4y \leq 12 \implies x + 2y \leq 6$$2$. $x + y \leq 3$$3$. $x \geq 0, y \geq 0$The vertices of the feasible region are found by the intersection of the lines:- Intersection of $x + y = 3$ and $x = 0$ gives $(0, 3)$.- Intersection of $x + y = 3$ and $y = 0$ gives $(3, 0)$.- The origin $(0, 0)$ is also a vertex.Evaluating $Z$ at the vertices:- At $(0, 0)$: $Z = 2(0) + 3(0) = 0$- At $(3, 0)$: $Z = 2(3) + 3(0) = 6$- At $(0, 3)$: $Z = 2(0) + 3(3) = 9$The minimum value of $Z$ is $0$ at the point $(0, 0)$.

The minimum value of $Z = 2x + 3y$ for the system of linear constraints: $2x + 4y \leq 12$,$x + y \leq 3$,$x \geq 0$,and $y \geq 0$ is . . . . . . .

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