Solve the problem.
-The demand for a certain type of modem is given by
$$p=480-x$$
Where $\mathrm{p}$ is the price when $\mathrm{x}$ units are demanded. Determine the price that will produce the maximum revenue. (Hint: First find the revenue $R(x)$, that would be obtained at a demand of $x$ ).
A) $\$ 260$
B) $\$ 240$
C) $\$ 48$
D) $\$ 480$

Question

Quizplus · Accepted Answer

The revenue function is $R(x) = x \cdot p = x(480-x)$. To find the maximum revenue, take the derivative $R'(x) = 480 - 2x$ and set it to zero: $480 - 2x = 0$. Solving gives $x = 240$. Substitute $x = 240$ back into the price equation $p = 480 - x$ to get $p = 240$.

Solve the Problem p=480−xp=480-xp=480−x Where p\mathrm{p}p Is the Price When x\mathrm{x}x Units Are Demanded

Solve the Problem $p=480-x$ Where $\mathrm{p}$ Is the Price When $\mathrm{x}$ Units Are Demanded