Answer:
(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