Question

you run a boutique bakery that specializes in gourmet cupcakes. the bakery’s fixed costs are $500 per month, and the variable cost to produce each cupcake is $2. the bakery’s revenue is $0 when you sell 0 cupcakes. due to market saturation, it is also $0 when you sell 150 cupcakes. your revenue reaches its maximum when you sell 75 cupcakes. write a linear cost function, c(x), and a quadratic revenue function, r(x), where x represents the number of cupcakes produced in a month. c(x)=□x + □ r(x)=-x(x - □)

Explanation:

Step1: Define linear cost function

A linear cost function has the form $C(x) = (\text{variable cost})x + (\text{fixed cost})$. Here, variable cost per cupcake is $\$2$, fixed cost is $\$500$.
$C(x) = 2x + 500$

Step2: Find quadratic revenue roots

Quadratic revenue has roots at $x=0$ and $x=150$ (revenue = $\$0$ at these points). A quadratic with roots $r_1, r_2$ is $R(x)=a(x-r_1)(x-r_2)$. We know $R(x) = -x(x - \square)$, so the second root is 150.
$R(x) = -x(x - 150)$

Answer:

$C(x) = 2x + 500$
$R(x) = -x(x - 150)$