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)

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

Quizplus · Accepted Answer

- Graphing the system of inequalities, we get a feasible region that is bounded by the x and y axes, as well as the two lines 2x+y=15 and x-3y=-3. 
- The corners of this feasible region are (0,0), (7.5,0), (6,3), and (2,5). 
- We can evaluate the objective function at each of these corners: 
  - (0,0) gives z=0
  - (7.5,0) gives z=22.5 
  - (6,3) gives z=33 
  - (2,5) gives z=21 
- Since we are looking for the maximum value of the objective function, we can see that the maximum occurs at (6,3) with a value of z=33. Therefore, the answer is A.

An Objective Function and a System of Linear Inequalities Representing