Question

1. Write a cost function for each situation. Identify all variables used. (a) A chain-saw rental firm charges $12 plus $1 per hour. (b) A trailer-hauling service charges $445 plus $2 per mile. (c) A parking garage charges 50¢ plus 35¢ per half-hour. (d) For a one-day rental, a car rental charges $44 plus 28¢ per mile.

Answer 1

Given:

The objective is to write cost function for each situation.

Explanation:

a)

The fixed charge is, f = $12.

The hourly charge is, h = $1.

Consider the number of hours as x. Then, the cost function can be written as,

$\begin{gathered} C(x)=f+hx \\ C(x)=12+(1)x \\ C(x)=12+x \end{gathered}$

Hence, the cost function is, C(x) = 12+x.

b)

The fixed charge is, f = $445.

The charge per mile is, h = $12.

Consider the number of miles as x. Then, the cost function can be written as,

$\begin{gathered} C(x)=f+hx \\ C(x)=445+12x \end{gathered}$

Hence, the cost function is, C(x) = 445+12x.

c)

The fixed charge is, f = 50¢.

The hourly charge is, h = 2(35¢) = 70¢.

Consider the number of hours as x. Then, the cost function can be written as,

$\begin{gathered} C(x)=f+hx \\ C(x)=50+70x \end{gathered}$

Hence, the cost function is, C(x) = 50+70x.

d)

The fixed charge is, f = $44.

The charge per mile is, h = 28¢ = $0.28.

Consider the number of miles as x. Then, the cost function can be written as,

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