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 $P = 3 x + 4 y$ what is the maximum profit?
A) 19
B) 20
C) 21
D) 22

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 $P = 3 x + 4 y$ what is the maximum profit?
A) 19
B) 20
C) 21
D) 22

Quizplus · Accepted Answer

To find the maximum profit, we first identify the corner points of the feasible region defined by the given constraints. The corner points can be found by solving the system of equations formed by the intersection of the constraints.1. Intersection of $x + y = 6$ and $x + 2y = 8$:   Solving these equations simultaneously, we get $x = 4, y = 2$.2. Intersection of $x + 2y = 8$ and $x = 0$:   Substituting $x = 0$, we get $2y = 8$, hence $y = 4$.3. Intersection of $x + y = 6$ and $y = 0$:   Substituting $y = 0$, we get $x = 6$.4. The origin $x = 0, y = 0$ is also a corner point but it will not give a maximum profit since both $x$ and $y$ are non-negative and the profit increases with $x$ and $y$.Now, we calculate the profit $P = 3x + 4y$ at each of these corner points:1. At $x = 4, y = 2$, $P = 3(4) + 4(2) = 12 + 8 = 20$.2. At $x = 0, y = 4$, $P = 3(0) + 4(4) = 16$.3. At $x = 6, y = 0$, $P = 3(6) + 4(0) = 18$.Among these, the maximum profit is $20$, which occurs at the point $x = 4, y = 2$. Therefore, the correct answer is $B) 20$.

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 $\begin{array} { l } x + y \leq 6 \\x + 2 y \leq 8 \\x \geq 0 \\y \geq 0\end{array}$