A pork-processing facility is considering installing either a storage facility or a holding pond. A biosystems engineer has been hired to evaluate the economic trade-offs for the two alternatives. The engineer estimates the cost of the storage facility to be \(\$ 213,000\), with annual costs for maintenance to be \(\$ 3,200\) per year. She estimates the cost of the pond to be \(\$ 90,000\), plus \(\$ 45,000\) for pumps and piping; annual operating and maintenance costs for the holding pond are estimated to be \(\$ 8,500\). The engineer estimates the life of the storage facility and the pond to be around 20 years but is concerned about the accuracy of this estimate. She decides to do a sensitivity analysis.

a. Develop the equation she should use to determine how sensitive the economic decision is to changes in life. Use a MARR of 15 percent.

b. Determine which alternative is preferred for lives ranging from 15 to 25 years in 1 year increments.