An Objective Function and a System of Linear Inequalities Representing

Multiple Choice

An objective function and a system of linear inequalities representing constraints are given. Graph the system of
inequalities representing the constraints. Find the value of the objective function at each corner of the graphed
region. Use these values to determine the maximum value of the objective function and the values of x and y for
which the maximum occurs.
- $$\begin{array} { l l } \text { Objective Function } & z = 7 x + 6 y \\\text { Constraints } & x \geq 0 \\& y \geq 0 \\& 3 x + y \leq 21 \\& x + y \leq 10 \\& x + 2 y \geq 12\end{array}$$

A) Maximum 65.5; at (5.5, 4.5)
B) Maximum 60; at (6, 3)
C) Maximum 68; at (8, 2)
D) Maximum 66; at (6, 4)