Question

the annual total revenue for a product is given by $r(x) = 72,000x - 9x^2$ dollars, where $x$ is the number of u maximize revenue, how many units must be sold? what is the maximum possible annual revenue?

to maximize revenue, \\(\square\\) units must be sold.
(simplify your answer.)

the maximum possible annual revenue is $\square$.
(simplify your answer.)

Explanation:

Step1: Identify quadratic coefficients

$R(x) = -9x^2 + 72000x$, so $a=-9$, $b=72000$

Step2: Find x for max revenue

Use vertex formula $x = -\frac{b}{2a} = -\frac{72000}{2(-9)} = 4000$

Step3: Calculate max revenue

Substitute $x=4000$ into $R(x)$: $R(4000) = -9(4000)^2 + 72000(4000) = 144000000$

Answer:

4000
144000000