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 $p=-0.25 x+49$ 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 $R=$

Step 1 ：Based on the results of an extensive market research study, an economist predicts that consumers in one market will buy \(x\) units per week of one model if the price is \(p=-0.25 x+49\) dollars.

Step 2 ：Recall that revenue is price times number of units sold. We can write an equation that represents the revenue the company will make \((R)\) from selling \(x\) units of the coffee maker in that market.

Step 3 ：The revenue is calculated by multiplying the price per unit by the number of units sold. In this case, the price per unit is given by the equation \(p=-0.25x+49\). Therefore, the revenue \(R\) can be calculated by multiplying this price by the number of units sold \(x\). This gives us the equation \(R=x(-0.25x+49)\).

Step 4 ：We can simplify the equation \(R=x(-0.25x+49)\) to \(R=-0.25x^2 + 49x\). This is the simplified form of the equation for the revenue \(R\) from selling \(x\) units.

Step 5 ：Final Answer: The simplified equation for the revenue \((R)\) from selling \(x\) units is given by \(R= \boxed{-0.25x^2 + 49x}\).