QuestionPractice Test Content Page 14 of 20
Question 14 5 Point
Assume that the linear cost and revenue models apply and let $x$ be the number of items.. An item costs $\$ 15$ to make. If fixed costs are $\$ 3700$ and profits are $\$ 4300$ when 200 items are made and sold, find then the revenue equation is: $$R(x)=\text { Blank } 1$$ (Please enter a simplified expression involving whole numbers and the variable x ) Blank 1 Add your answer

Studdy Solution
Use the given profit information to find the revenue equation. We know that when 200 items are made and sold, the profit is \$4300.
Substitute the known values into the profit equation:
$$4300 = R(200) - C(200)$$
First, calculate $C(200)$:
$$C(200) = 3700 + 15 \times 200$$ $$C(200) = 3700 + 3000$$ $$C(200) = 6700$$
Now substitute back into the profit equation:
$$4300 = R(200) - 6700$$
Solve for $R(200)$:
$$R(200) = 4300 + 6700$$ $$R(200) = 11000$$
Since the revenue function $R(x)$ is linear, it can be expressed as:
$$R(x) = mx$$
We know that $R(200) = 11000$, so:
$$11000 = m \times 200$$
Solve for $m$:
$$m = \frac{11000}{200}$$ $$m = 55$$
Thus, the revenue equation is:
$$R(x) = 55x$$