# If the price from the sale of x-units is given by p = 100 x - x^2, find the revenue function.

## Question:

If the price from the sale of x-units is given by {eq}p = 100 x - x^2 {/eq}, find the revenue function.

## Revenue Function

Revenue is defined as as a total income earned selling **x** products at some given price **p**. Let's assume that price is dependent on the number of units sold and is given by a function **p(x)**. Multiplying the number of units sold **x** by the price function **p(x)** would correspond to the revenue function **R(x)**.

## Answer and Explanation:

In our problem, we're given:

{eq}p(x) = 100x - x^2 {/eq}

Multiplying our price function by the number of units sold, **x**, we will obtain the revenue function:

{eq}R(x) = xp(x) = x(100x - x^2) = -x^3 + 100x^2 {/eq}

Therefore, the revenue function in this problem corresponds to {eq}\boxed{R(x) = -x^3 + 100x^2} {/eq}.

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from Financial Accounting: Help and Review

Chapter 5 / Lesson 27