A specialized machine essential for a company's operations costs $16,000 and has operating costs of $2,000 the first year. The operating costs increase by $1,000 each year thereafter. We assume that the operating costs occur at the end of each year. The annual interest rate is 6% and the company plans to stay in operation forever.

You have an option to replace the machine periodically after a period of n years, where n must be an integer. The replacement cost is $16,000. Your objective is to select the replacement period n such that the present value of the total cost is minimized. Assume that due to its specialized nature, the machine has no salvage value.

What is the optimal replacement period, n? Note n must be an integer.