Refer to the feasible region defined by the following constraints to answer the following questions :
$\begin{array} { l }
x + y \leq 6 \
x + 2 y \leq 8 \
x \geq 0 \
y \geq 0
\end{array}$
-If the profit formula is $P = 5 x$ what is the maximum profit?
A) 30
B) 32
C) 35
D) 40

Question

Refer to the feasible region defined by the following constraints to answer the following questions : 
$\begin{array} { l } 
x + y \leq 6 \
x + 2 y \leq 8 \
x \geq 0 \
y \geq 0
\end{array}$
-If the profit formula is $P = 5 x$ what is the maximum profit?
A) 30
B) 32
C) 35
D) 40

Quizplus · Accepted Answer

The maximum profit occurs at the corner point of the feasible region that maximizes the profit formula. The feasible region is defined by the intersection of the given constraints. To find the maximum profit, we substitute the corner points of the feasible region into the profit formula $P = 5x$. The corner points of the feasible region can be found by solving the system of equations formed by the intersection of the constraints. The corner points are (0,0), (0,4), (4,2), and (6,0). Substituting these into the profit formula gives profits of 0, 0, 20, and 30, respectively. Therefore, the maximum profit is 30.

Refer to the Feasible Region Defined by the Following Constraints x+y≤6x+2y≤8x≥0y≥0\begin{array} { l } x + y \leq 6 \\x + 2 y \leq 8 \\x \geq 0 \\y \geq 0\end{array}x+y≤6x+2y≤8x≥0y≥0​

Refer to the Feasible Region Defined by the Following Constraints $\begin{array} { l } x + y \leq 6 \\x + 2 y \leq 8 \\x \geq 0 \\y \geq 0\end{array}$