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.
- $$\begin{array} { l l } \text { Objective Function } & \mathrm { z } = 3 \mathrm { x } + 5 \mathrm { y } \\\text { Constraints } & \mathrm { x } \geq 0 \\& \mathrm { y } \geq 0 \\& 2 x + y \leq 15 \\& x - 3 y \geq - 3\end{array}$$

A) Maximum 33; at (6, 3)
B) Maximum 75; at (0, 15)
C) Maximum 22.5; at (7.5, 0)
D) Maximum 38; at (6, 4)