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)

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.
-$$\begin{array} { l l } 
\text { Objective Function } & z = 7 x + 6 y \
\text { Constraints } & x \geq 0 \
& y \geq 0 \
& 3 x + y \leq 21 \
& x + y \leq 10 \
& x + 2 y \geq 12
\end{array}$$
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)

Quizplus · Accepted Answer

Graphing the system of inequalities results in the following:
![Graph](https://i.imgur.com/afZN1rA.png)
The corners of the feasible region are (0,0), (7,0), (5.5,4.5) and (2,10). Evaluating the objective function at each of these corners yields:
(0,0): z = 0
(7,0): z = 42
(5.5,4.5): z = 65.5 (max)
(2,10): z = 52
Therefore, the maximum value of the objective function is 65.5, which occurs at (5.5,4.5). Thus, the answer is A.

An Objective Function and a System of Linear Inequalities Representing