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(D) The feasible region is unbounded as shown in the figure. The vertices of the feasible region are $(0, 4)$ and $(12, 6)$.We evaluate the objective

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does not exist

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(D) The feasible region is unbounded as shown in the figure. The vertices of the feasible region are $(0, 4)$ and $(12, 6)$.We evaluate the objective function $z = 3x - 4y$ at these vertices:At $(0, 4)$,$z = 3(0) - 4(4) = -16$.At $(12, 6)$,$z = 3(12) - 4(6) = 36 - 24 = 12$.Since the region is unbounded,we check if $z  3x + 16$,or $y > \frac{3}{4}x + 4$. Since the feasible region extends infinitely in the direction where $y$ increases relative to $x$,there exist points in the region that satisfy this inequality. Therefore,the minimum value does not exist.

The feasible region for an $LPP$ is shown in the figure. Let $z = 3x - 4y$ be the objective function. The minimum value of $Z$ is:

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