Question 21 of 25
$(4$ points)
Attempt 1 of 1
(1) $1 \mathrm{~h} 46 \mathrm{~m}$ Remaining
4-8 Write a profit equation given cost and revenue equations (Application 2)
The revenue made from selling $x$ units of a coffee maker is given by $R=-0.31 x^{2}+55 x$. It costs the manufacturer $C=-0.14 x^{2}+14 x+860$ dollars to make $x$ units of this particular coffee maker. Write an equation describing the profit $(P)$ made from selling $x$ units of the coffee maker in this market. Enter your answer in simplified form.
The simplified equation for the profit $(P)$ from selling $x$ units is given by:
\[
P=
\]
Answer
So, the simplified equation for the profit \(P\) from selling \(x\) units is given by \(\boxed{P=-0.17x^{2}+41x-860}\).
Step 1 ：Given the revenue equation \(R=-0.31x^{2}+55x\) and the cost equation \(C=-0.14x^{2}+14x+860\).
Step 2 ：The profit equation is calculated by subtracting the cost from the revenue.
Step 3 ：So, \(P=R-C\).
Step 4 ：Substituting the given equations into the profit equation, we get \(P=(-0.31x^{2}+55x)-(-0.14x^{2}+14x+860)\).
Step 5 ：Simplifying the equation, we get \(P=-0.17x^{2}+41x-860\).
Step 6 ：So, the simplified equation for the profit \(P\) from selling \(x\) units is given by \(\boxed{P=-0.17x^{2}+41x-860}\).
