Question

1. the graph shows the cost (solid line) and revenue (dashed line) of a small printing business offering custom posters during its first eight months of operation

write equations to represent the cost and the revenue functions for this business.

Explanation:

Step1: Define cost function form

Cost function is linear: $C(x)=mx+b$, where $b$ is fixed cost.

Step2: Find cost function parameters

Use points $(0,120)$ and $(4,240)$.
$b=120$, $m=\frac{240-120}{4-0}=30$.
So $C(x)=30x+120$.

Step3: Define revenue function form

Revenue function is linear: $R(x)=kx$, no fixed cost.

Step4: Find revenue function parameter

Use point $(4,240)$.
$k=\frac{240-0}{4-0}=60$.
So $R(x)=60x$.

Answer:

Cost function: $C(x)=30x+120$
Revenue function: $R(x)=60x$