Textbook Problem

VanBuren Metals is a manufacturing company that uses many large machines to work on metals. These machines require frequent maintenance because of wear and tear, and VanBuren finds that it is sometimes advantageous, from a cost standpoint, to replace machines rather than continue to maintain them. For one particular class of machines, the company has estimated the quarterly costs of maintenance, the salvage value from reselling an old machine, and the cost to purchase a new machine.⁷ We assume that the maintenance cost and the salvage value depend on the age of the current machine (at the beginning of the quarter). However, we assume that the maintenance costs, the salvage values, and the purchase cost do not depend on time. In other words, we assume no inflation. Specifically, we assume the following:

• The purchase cost of a new machine is always $3530.
• The maintenance cost of a machine in its first quarter of use is $100. For each succeeding quarter, the maintenance cost increases by $65. This reflects the fact that machines require more maintenance as they age.
• The salvage value of a machine after one quarter of use is $1530. After each succeeding quarter of use, the salvage value decreases by $110.

VanBuren wants to devise a strategy for purchasing machines over the next five years. As a matter of policy, the company never sells a machine that is less than one year old, and it never keeps a machine that is more than three years old. Also, the machine in use at the beginning of the current quarter is brand new.

In the VanBuren machine replacement problem, suppose the company starts with a machine that is eight quarters old at the beginning of the first quarter. Modify the model appropriately, keeping in mind that this initial machine must be sold no more than four quarters from now.