Find the Minimum and Maximum Values of the Objective Function $$\left\{ \begin{array} { l } y \geq 0 \\x - y \geq - 2 \\2 x + 3 y \geq 6 \\5 x + 2 y \leq 25\end{array} \right.$$

Multiple Choice

Find the minimum and maximum values of the objective function and where it occurs, subject to the indicated constraints. Objective function:
Z = 3x + 4y
Constraints: $$\left\{ \begin{array} { l } y \geq 0 \\x - y \geq - 2 \\2 x + 3 y \geq 6 \\5 x + 2 y \leq 25\end{array} \right.$$

A) minimum = 8 at (0, 2) ; maximum = 29 at (3, 5)
B) minimum = -11 at (3, 5) ; maximum = 15 at (5, 0)
C) minimum = 8 at (0, 2) ; maximum = 27 at (3, 5)
D) minimum = 0 at (0, 0) ; maximum = 29 at (3, 5)
E) minimum = 9 at (3, 0) ; maximum = 15 at (5, 0)