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(D) First,we graph the feasible region of the system of inequalities $(2)$ to $(5)$.The feasible region is unbounded as shown in the figure.We evaluat

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No minimum value

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(D) First,we graph the feasible region of the system of inequalities $(2)$ to $(5)$.The feasible region is unbounded as shown in the figure.We evaluate $Z$ at the corner points:Corner Point$Z = -50x + 20y$$(0, 5)$$100$$(0, 3)$$60$$(1, 0)$$-50$$(6, 0)$$-300$From the table,the smallest value obtained at a corner point is $-300$ at $(6, 0)$.Since the feasible region is unbounded,we must check if $-300$ is the true minimum.We graph the inequality $-50x + 20y If this open half-plane has common points with the feasible region,then $-300$ is not the minimum value.As seen in the graph,the line $-5x + 2y = -30$ passes through the feasible region,and the region $-5x + 2y Therefore,the objective function $Z = -50x + 20y$ has no minimum value subject to the given constraints.

Determine graphically the minimum value of the objective function
$Z = -50x + 20y$ .....$(1)$
subject to the constraints:
${2x - y \geqslant -5}$ .....$(2)$
${3x + y \geqslant 3}$ .....$(3)$
${2x - 3y \leqslant 12}$ .....$(4)$
${x \geqslant 0, y \geqslant 0}$ .....$(5)$

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Determine graphically the minimum value of the objective function$Z = -50x + 20y$ .....$(1)$subject to the constraints:${2x - y \geqslant -5}$ .....$(2)$${3x + y \geqslant 3}$ .....$(3)$${2x - 3y \leqslant 12}$ .....$(4)$${x \geqslant 0, y \geqslant 0}$ .....$(5)$