1. Suppose you have the problem of delivering 500 lb. boxes from Washington, D.C. to Baltimore and are considering the purchase of a truck. You have in mind either a small truck (capacity of 1,500 lbs. and a cost of $2,00 a year) or a large truck (capacity of 4,000 lbs. and a cost of $10,000 a year). The cost of gasoline, maintenance, and the driver is $24 per round trip for either truck. You may assume that the trucks run at capacity, rather than taking partial loads.

1. Write the total cost functions for each truck in terms of the quantity of boxes carried per year.
2. At what quantity of boxes would you switch from a small truck to a large truck? N
3. Suppose that for all trips in excess of 300 per year, there is an overtime cost of $10 per round trip. You expect to deliver 1200 boxes per year. What is the total annual cost of each mode of delivery? N

2. As an administrator of a law firm, you are trying to determine whether or not to outsource

the responsibilities of managing your administrative assistants. If you manage the responsibilities,

each assistant will cost your firm $50,000 a year. There is one assistant for every lawyer in your

firm. You will also be required to hire an administrator to manage the assistants at $75,000 a year

regardless of how many lawyers you have. Finally, you will also have to employ a temporary work

agency to fill in for any vacationing or sick assistant at a cost of $200,000 a year regardless of how

many lawyers you have. If, on the other hand, you outsource your operations, it will cost you

$60,000 a year for each assistant but there are no additional management or temporary employment

agency fees because the company with which you outsource takes care of this.

1. Write total cost functions for each of the two options.
2. What is the critical size of your law firm where you switch from on option to the other? N