John Smith is responsible for periodically buying new trucks to replace older trucks in his company's fleet of vehicles. He is expected to determine the time a truck should be retained so as to minimize the average cost of owning the truck. Assume the purchase price of a new truck is $9000 with trade-in. Also assume the maintenance cost (in dollars) per truck for t years can be expressed analytically by the following empirical model:

where t is the time in years that the company owns the truck.

a. Determine E(t), the total cost function for a single truck retained for a period of t years.

b. Determine E_A(t), the average annual cost function for a single truck that is kept in the fleet for t years.

c. Graphically depict E_A(t) as a function of t. Justify the shape of your graph.

d. Analytically determine t^∗, the optimal period that a truck should be retained in the fleet. Remember that the objective is to minimize the average cost of owning a truck.

e. Suppose we have to round t^∗ to the nearest whole year. In general, would it be better to round up or round down? Justify your answer.

Transcribed Image Text:

C(t) = 640 + 180(t + 1)t