The objective function z = 4x + 5y subject to | vedclass

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(B) The constraints are $2x + y \geq 7$,$2x + 3y \leq 15$,$y \leq 3$,$x \geq 0$,and $y \geq 0$. From the graph,the vertices of the feasible region are

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on the $X$-axis

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(B) The constraints are $2x + y \geq 7$,$2x + 3y \leq 15$,$y \leq 3$,$x \geq 0$,and $y \geq 0$. From the graph,the vertices of the feasible region are $A(3.5, 0)$,$B(7.5, 0)$,$C(3, 3)$,and $D(2, 3)$. We evaluate the objective function $z = 4x + 5y$ at these vertices: $z(A) = 4(3.5) + 5(0) = 14 + 0 = 14$ $z(B) = 4(7.5) + 5(0) = 30 + 0 = 30$ $z(C) = 4(3) + 5(3) = 12 + 15 = 27$ $z(D) = 4(2) + 5(3) = 8 + 15 = 23$ The minimum value is $14$,which occurs at point $A(3.5, 0)$. Since point $A$ lies on the $X$-axis,the minimum value occurs on the $X$-axis.

The objective function $z = 4x + 5y$ subject to the constraints $2x + y \geq 7$,$2x + 3y \leq 15$,$y \leq 3$,$x \geq 0$,and $y \geq 0$ has a minimum value at which point?

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