Question

A rental company purchases a truck for $17,500. The truck requires an average cost of $4.75 per day in maintenance.

(a) Find a linear function that expresses the total cost C of owning the truck after t days.
C(t) =

(b) The truck rents for $55.00 a day. Find a linear function that expresses the revenue R when the truck has been rented for t days.
R(t) =

(c) The profit after t days, P(t), is given by the function P(t) = R(t) = C(t). Find the linear function P(t).
P(t) =

(d) Use the function P(t) that you obtained in part (c) to determine how many days it will take the company to break even on the purchase of the
truck. Assume that the truck is in use every day. (Round your answer to the nearest day.)
days

Answer 1

(a) The total cost C of owning the truck after t days can be expressed as the sum of the purchase price and the maintenance cost over the number of days of ownership:

C(t) = 17500 + 4.75t

(b) The revenue R when the truck has been rented for t days can be expressed as the rental rate times the number of days rented:

R(t) = 55t

(c) The profit after t days is given by the equation P(t) = R(t) - C(t). Substituting the expressions for R(t) and C(t) from parts (a) and (b), we get:

P(t) = 55t - (17500 + 4.75t)

Simplifying,

P(t) = 50.25t - 17500

(d) The company will break even when the profit is zero. So, we need to solve the equation P(t) = 0 for t:

50.25t - 17500 = 0

Solving for t, we get:

t = 348.26

Rounding to the nearest day, the company will break even after 348 days of use