The price $p$ (in dollars) and the quantity $x$ sold of a certain product satisfy the demand equation $x=-8 p+800$. Answer parts (a) through $(\mathrm{g})$.
(a) Find a model that expresses the revenue $R$ as a function of $p$. (Remember, $R=x p$.)
\[
R(p)=
\]
(Simplify your answer. Use integers or decimals for any numbers in the expression.)
Answer
Final Answer: The model that expresses the revenue \(R\) as a function of \(p\) is \(\boxed{8p(100 - p)}\).
Step 1 ：Given the demand equation \(x=-8p+800\).
Step 2 ：Remember that the revenue \(R\) is the product of the price \(p\) and the quantity \(x\) sold, so \(R=xp\).
Step 3 ：We can substitute the demand equation into the revenue equation to express \(R\) as a function of \(p\).
Step 4 ：Substituting \(x\) into the revenue equation, we get \(R = p(800 - 8p)\).
Step 5 ：Simplify the equation to get \(R = 8p(100 - p)\).
Step 6 ：Final Answer: The model that expresses the revenue \(R\) as a function of \(p\) is \(\boxed{8p(100 - p)}\).
