Find the Maximum Value of the Objective Function and Where $z = 6 x - 7 y$

Multiple Choice

Find the maximum value of the objective function and where it occurs, subject to the indicated constraints. (You should graph the feasible solutions on the grid below before you attempt to find the minimum and maximum values.) Objective function: $z = 6 x - 7 y$ Constraints: $$\left\{ \begin{array} { l } x \geq 0 \\y \geq 0 \\5 x + 4 y \leq 20 \\3 x + 2 y \leq 6\end{array} \right.$$

A) $\text { maximum } = 24 \text { at } ( 4,0 )$
B) $\text { maximum } = 12 \text { at } ( 2,0 )$
C) $\text { maximum } = 35 \text { at } ( 0,5 )$
D) $\text { The maximum is unbounded. }$
E) $\text { There is no maximum. The feasable solution set is empty. }$