Question

ear-quadratic systems
modeling a company’s revenue and cost
a company’s revenue, ( r(x) ), in thousands of dollars, from selling ( x ) thousand units is modeled by ( r(x) = -2x^2 + 12x ), and its cost, ( c(x) ), in thousands of dollars, is modeled by ( c(x) = 4x ).
how many units need to be sold to maximize the company’s revenue?
3,000 units
2,000 units
6,000 units
4,000 units

Explanation:

Step1: Identify vertex formula for parabola

For quadratic $ax^2+bx+c$, vertex $x=-\frac{b}{2a}$

Step2: Plug in revenue coefficients

$a=-2$, $b=12$: $x=-\frac{12}{2(-2)}$

Step3: Calculate x value

$x=\frac{-12}{-4}=3$

Step4: Convert to actual units

$x=3$ thousand units = 3,000 units

Answer:

3,000 units