Question

daniella manages a flower shop. the fixed costs are $500 per month, and each bouquet costs $5 to make. the revenue is $0 when no bouquets are sold and $0 when 120 bouquets are sold due to limited demand. the maximum revenue occurs when 60 bouquets are sold. write a linear cost function, c(x), and a quadratic revenue function, r(x), where x represents the number of bouquets sold.
c(x) = \square x + \square
r(x) = -x(x - \square)

Explanation:

Step1: Define linear cost function

A linear cost function has the form $C(x) = \text{variable cost per unit} \cdot x + \text{fixed costs}$. The variable cost per bouquet is $\$5$, fixed costs are $\$500$.
$C(x) = 5x + 500$

Step2: Find roots of revenue function

The revenue is $\$0$ when $x=0$ and $x=120$, so these are the roots of the quadratic $R(x)$. A quadratic with roots $r_1$ and $r_2$ can be written as $R(x) = ax(x-r_2)$.
Roots: $x=0$ and $x=120$

Step3: Confirm quadratic revenue form

Given $R(x) = -x(x - \square)$, substitute the non-zero root $120$ into the expression.
$R(x) = -x(x - 120)$

Answer:

$C(x) = 5x + 500$
$R(x) = -x(x - 120)$