Question

the demand $d$ for a companys product at cost $x$ is predicted by the function $d(x) = 500 - 2x$. the price $p$ in dollars that the company can charge for the product is given by $p(x) = x + 5$.
use the formula revenue = price × demand to find the revenue function for the product.
$r(x) = \square + \square x - \square x^2$

Explanation:

Step1: Recall revenue formula

$R(x) = p(x) \times d(x)$

Step2: Substitute given functions

$R(x) = (x + 5)(500 - 2x)$

Step3: Expand the product

$R(x) = x(500) + x(-2x) + 5(500) + 5(-2x)$
$R(x) = 500x - 2x^2 + 2500 - 10x$

Step4: Combine like terms

$R(x) = 2500 + (500x - 10x) - 2x^2$
$R(x) = 2500 + 490x - 2x^2$

Answer:

$R(x) = 2500 + 490x - 2x^2$
(The blanks are filled with 2500, 490, and 2 respectively)