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}.


Learn more about this topic:

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How to Calculate Sales Revenue: Definition & Formula

from Financial Accounting: Help and Review

Chapter 5 / Lesson 27
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