Question

company revenue
a company’s revenue, $r(x) = -0.4x^2 + 6x$, in thousands of dollars, from selling $x$ thousand units, and its cost, $c(x) = 2x$, thousands of dollars.
how many units need to be sold to maximize the company’s revenue?
7,500 units
22,500 units
20,000 units

Explanation:

Step1: Identify revenue function

The revenue function is given as $R(x) = -0.4x^2 + 6x$, where $x$ is thousands of units.

Step2: Find vertex of quadratic

For a quadratic $ax^2+bx+c$, vertex $x$-value is $x=-\frac{b}{2a}$. Here $a=-0.4$, $b=6$.
$x = -\frac{6}{2\times(-0.4)} = \frac{6}{0.8} = 7.5$

Step3: Convert to actual units

$x$ is thousands of units, so total units = $7.5 \times 1000 = 7500$.

Answer:

7,500 units