Solve the problem.
-The price $p$ (in dollars) and the quantity $x$ sold of a certain product obey the demand equation
$$p = - 10 x + 240 , \quad 0 \leq x \leq 24 \text {. }$$
What price should the company charge to maximize revenue?
A) \$6
B) $\$ 18$
C) $\$ 14.4$
D) $\$ 12$

Question

Quizplus · Accepted Answer

Revenue $R$ is given by $R = p \times x = (-10x + 240)x$. To maximize revenue, differentiate $R$ with respect to $x$ and set the derivative equal to zero. The derivative of $R$ with respect to $x$ is $-20x + 240$. Setting this equal to zero gives $x = 12$. Substituting $x = 12$ into the demand equation gives $p = -10(12) + 240 = 120$, which means the price should be \$12 to maximize revenue.

Solve the Problem ppp (In Dollars) and the Quantity xxx Sold of a Certain Product Obey the Demand Equation

Solve the Problem $p$ (In Dollars) and the Quantity $x$ Sold of a Certain Product Obey the Demand Equation