Please assist with the given problem regarding upgrading manufacturing facilities.
Task: You are considering upgrading some manufacturing facilities by purchasing one of three different machines, each with the same production capacity. Machine a costs $30,000, has a life of 40 years, annual maintenance costs of $1500, and salvage value of $5000. Machine b costs $20,000, has a life of 20 years, annual maintenance of $2000 and salvage value of $3000. Machine c costs $10,000 has a life of 10 years annual maintenance of $4000 and no salvage value. Determine the most economical choice based on minimizing the present value of total costs. Use an annual discount rate of 10%. Assume that initial costs, annual maintenance, and discount rates are constant throughout the analysis period.