Question

A company's marketing department has determined that if their product is sold at the price of p dollars per unit, they can sell q=1000−100p units. Each unit costs 7 dollars to make.

Answer 1

Given:

A company's marketing department has determined that if their product is sold at the price of p dollars per unit, they can sell q=1000−100p units. Each unit costs 7 dollars to make.

Required:

Solve part a and b.

Explanation:

Part A.

$\begin{gathered} Revenue=R=Price\times Quality \\ =pq \\ =1000p-100p^2 \\ \text{ Take the derivative, set equal to zero and solve for p} \\ R^{\prime}=1000-200p \\ 1000-200p=0 \\ 200p=1000 \\ p=5 \end{gathered}$

Part B.

To maximize profits, you need

$\begin{gathered} Profit=Revenue-cost \\ =1000p-100p^2-7(1000-100p) \\ =1700p-100p^2-7000 \\ \text{ Take the derivative, set it equal to zero and solve for p} \\ 1700-200p=0 \\ 200p=1700 \\ p=8.5 \end{gathered}$

Answer:

answered the question.