Solve the problem.
-Find the number of units that must be produced and sold in order to yield the maximum profit, given the follow equations for revenue and cost:
$\begin{array} { l }
R ( x ) = 30 x - 0.5 x ^ { 2 } \
C ( x ) = 2 x + 8
\end{array}$
A) 28 units
B) 32 units
C) 36 units
D) 29 units

Question

Solve the problem.
-Find the number of units that must be produced and sold in order to yield the maximum profit, given the follow equations for revenue and cost:
$\begin{array} { l } 
R ( x ) = 30 x - 0.5 x ^ { 2 } \
C ( x ) = 2 x + 8
\end{array}$
A) 28 units
B) 32 units
C) 36 units
D) 29 units

Quizplus · Accepted Answer

To find the maximum profit, we first find the profit function $P(x) = R(x) - C(x)$. This gives $P(x) = (30x - 0.5x^2) - (2x + 8) = -0.5x^2 + 28x - 8$. The maximum profit occurs at the vertex of this parabola, which is at $x = -\frac{b}{2a}$. Here, $a = -0.5$ and $b = 28$, so $x = -\frac{28}{2(-0.5)} = 28$. Thus, 28 units must be produced and sold for maximum profit.

Solve the Problem R(x)=30x−0.5x2C(x)=2x+8\begin{array} { l } R ( x ) = 30 x - 0.5 x ^ { 2 } \\C ( x ) = 2 x + 8\end{array}R(x)=30x−0.5x2C(x)=2x+8​

Solve the Problem $\begin{array} { l } R ( x ) = 30 x - 0.5 x ^ { 2 } \\C ( x ) = 2 x + 8\end{array}$