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:
$\begin{array} { l }
R ( x ) = 2 x \
G ( x ) = 0.01 x ^ { 2 } + 0.9 x + 40
\end{array}$
A) 55 units
B) 145 units
C) 110 units
D) 290 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:
$\begin{array} { l } 
R ( x ) = 2 x \
G ( x ) = 0.01 x ^ { 2 } + 0.9 x + 40
\end{array}$
A) 55 units
B) 145 units
C) 110 units
D) 290 units

Quizplus · Accepted Answer

The correct answer is A because the maximum profit occurs when the marginal revenue equals the marginal cost. The marginal revenue is the derivative of the revenue function, and the marginal cost is the derivative of the cost function. The derivative of the revenue function is 2, and the derivative of the cost function is 0.02x + 0.9. Setting these two derivatives equal to each other, we get 2 = 0.02x + 0.9, which gives us x = 55. Therefore, the number of units that must be produced and sold in order to yield the maximum profit is 55.

Solve the Problem R(x)=2xG(x)=0.01x2+0.9x+40\begin{array} { l } R ( x ) = 2 x \\G ( x ) = 0.01 x ^ { 2 } + 0.9 x + 40\end{array}R(x)=2xG(x)=0.01x2+0.9x+40​

Solve the Problem $\begin{array} { l } R ( x ) = 2 x \\G ( x ) = 0.01 x ^ { 2 } + 0.9 x + 40\end{array}$