SOLUTION: A rental company purchases a truck for $19,500. The truck requires an average cost of $6.75 per day in the maintenance. (a)Find a linear function that expresses the total cost

Question 109703This question is from textbook College Algebra
: A rental company purchases a truck for $19,500. The truck requires an average cost of $6.75 per day in the maintenance.
(a)Find a linear function that expresses the total cost C of owning the truck after t days.
(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.
(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)
(d)Use the function P(t) that you obtained in '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 everyday. This question is from textbook College Algebra

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
The cost of the truck must be what was paid at the start ($19,500) plus what it costs per day to operate ($6.75) times the number of days:
:

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Revenue is just what you make per day ($55), times the number of days:
:

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Now, profit is equal to revenue minus cost, or as given:
:
, or substituting our definitions of R(t) and C(t) we get:
:

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Breakeven is the point where the profit function, P(t) is 0. That means that you can set the expression for P(t) equal to zero and solve for t:
:

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Since the question asks how many days it will take the company to break even, you can presume that the desired answer is an integer, therefore, round the answer up to 405. You have to round up because at the end of the 404th day, P(404) < 0 (just slightly less), so it isn't until the end of the next day when the customer on the 405th day pays his bill that the P(t) function actually goes positive.

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