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

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

Step-by-step 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:

`-(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} -(1800)/(2(-100)) \\ \Rightarrow-(1800)/(-200) \\ \Rightarrow(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}`