Total company purchases a truck for $13,500. The truck requires an average cost

Question

Total company purchases a truck for $13,500. The truck requires an average cost $9.75 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 $58,00 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 R will take the company to break even on the purchases of the truck. Assume that the truck is in use every day. (Round your answer to the nearest day.)

Explanation / Answer

Fixed cost of truck= $13500

Avg cost per day = $ 9.75

C(t) = 13500 +9.75t

Revenue function: rent per day = $56

R(t) = 56t

Profit = Revenue - Cost = 56t - ( 13500 +9.75t)

= - 13500 + 46.25t

Break even :

Profit =0

0= - 13500 + 46.25t

t = 13500/46.25 = 291.89 = 292 days

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