Problem
Question 20 of 25 (4 points) Attempt 1 of 1 (J) $1 \mathrm{~h} 43 \mathrm{~m}$ Remaining 4-8 Write a revenue equation given a price equation (Application 1) Based on the results of an extensive market research study that I totally made up, an economist hired by a company that makes a popular line of inexpensive coffee makers predicts that consumers in one market will buy $x$ units per week of one model if the price is $p=-0.22 x+46$ dollars. Recall that revenue is price times number of units sold. Write an equation that represents the revenue the company will make ( $R)$ from selling $x$ units of the coffee maker in that market. Enter your answer in simplified form. The simplified equation for the revenue $(R)$ from selling $x$ units is given by $R=$
Solution
Step 1 ：The revenue equation is given by the product of the price and the quantity sold. In this case, the price is given by the equation \(p=-0.22x+46\) and the quantity sold is \(x\). Therefore, the revenue equation will be \(R = p \cdot x = (-0.22x + 46) \cdot x\).
Step 2 ：Substitute \(p\) into the equation for \(R\), we get \(R = -0.22x^2 + 46x\).
Step 3 ：\(\boxed{R = -0.22x^2 + 46x}\) is the simplified equation for the revenue \(R\) from selling \(x\) units.
