Your company anticipates a need for the following number of DNA sequencing machines over the next 10 weeks.
At the beginning of each week you decide how many new machines to order at a cost of $20,000 each. Ordered machines arrive at the beginning of the next week. In your experience, each machine in your possession has an independent 5% chance of breaking down in any given week. You do not discover which machines are going to break during a week until after you have placed your order for new machines. For simplicity, assume that broken-down machines are complete "write-offs" and have no value. If, after breakdowns, you do not have enough machines to meet your requirements for the week, you incur a $5,000 cost for each machine you are "short" for the week (this cost is incurred because you must subcontract out your DNA sequencing work to other companies). Any machines still working at the end of the 10-week period are assumed to have a salvage value of $13,000 each. You currently have 11 machines in your possession and you have room for at most 25. Assume that your firm's internal discount rate is 1% per week.
Determine the machine-buying policy that minimizes the expected present value of your costs for the 10-week period, net of the present value of the ending salvage value.