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.
-$$\begin{array} { l l }
\text { Objective Function } & z = 7 x - 6 y \
\text { Constraints } & x \geq 0 \
& 0 \leq y \leq 5 \
& x - y \leq 9 \
& x + 2 y \leq 12
\end{array}$$
A)Maximum: 64; at (10, 1)
B)Maximum: 63; at (9, 0)
C)Maximum: -16; at (2, 5)
D)Maximum: -30; at (0, 5)

Question

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.
-$$\begin{array} { l l } 
\text { Objective Function } & z = 7 x - 6 y \
\text { Constraints } & x \geq 0 \
& 0 \leq y \leq 5 \
& x - y \leq 9 \
& x + 2 y \leq 12
\end{array}$$
A)Maximum: 64; at (10, 1)
B)Maximum: 63; at (9, 0)
C)Maximum: -16; at (2, 5)
D)Maximum: -30; at (0, 5)

Quizplus · Accepted Answer

First, we graph the four inequalities to find the feasible region:

We can see that the feasible region is a quadrilateral with vertices at (0,0), (0,5), (3,6), and (10,1). 
Next, we evaluate the objective function at each vertex:

- (0,0): z = 7(0) - 6(0) = 0
- (0,5): z = 7(0) - 6(5) = -30
- (3,6): z = 7(3) - 6(6) = -9
- (10,1): z = 7(10) - 6(1) = 64

The maximum value of the objective function occurs at (10,1) with a value of 64. Therefore, the answer is choice A.

An Objective Function and a System of Linear Inequalities Representing