Question

A company that manufactures flash drives knows that the number of drives x it can sell each week is related to the price, p, in dollars, of each drive by the equation x = 1800 - 100p.a. Find the price p that will bring in the maximum revenue. Remember, revenue (R) is the product of price (p) and items sold (x), in other words, R = xp.The price $ will yield the max revenue.b. Find the maximum revenue.The max revenue is $

Answer 1

ANSWER

$\begin{gathered} (a)\ 9 \\ (b)\ 8,100 \end{gathered}$

EXPLANATION

(a) The revenue is gotten by finding the product of price and items sold.

Therefore, the revenue is:

$\begin{gathered} R=x\cdot p \\ R=(1800-100p)\cdot p \\ R=1800p-100p^2 \end{gathered}$

The function above is a quadratic function.

The find the price that will bring in the maximum revenue, we have to find the maximum value of the function.

The maximum value of a quadratic function is gotten by finding:

$-\frac{b}{2a}$

where a is the coefficient of p² and b is the coefficient of p.

Therefore, we have that the price at which the revenue is maximum is:

$\begin{gathered} -\frac{1800}{2(-100)} \\ \Rightarrow-\frac{1800}{-200} \\ \Rightarrow\frac{1800}{200} \\ \Rightarrow\ 9 \end{gathered}$

That is the answer.

(b) The maximum revenue is the value of the revenue at the maximum price.

Therefore, the maximum revenue is:

$\begin{gathered} R=(1800\cdot9)-(100\cdot9^2) \\ R=16200-8100 \\ R=\ 8,100 \end{gathered}$