A building can be air-conditioned by piping chilled water from an existing central refrigeration plant. Two proposals are being evaluated:

- Proposal 1: Uses 6 inch pipe to carry the chilled water, a water pump for 6 inch pipe, and a 30 horsepower motor to drive the pump. The installed cost of the 6 inch pipe and pump is $4000; the installed cost of the motor to drive the pump is $500; the salvage value of the system in 10 years is $500; and the energy cost per hour of operation is $0.40. The pump will have to be rebuilt at the end of year 6 at a cost of $300.

- Proposal 2: Uses 8 inch pipe to carry the chilled water, a water pump for 8 inch pipe, and a 15 horsepower motor to drive the pump. The installed cost of the 8 inch pipe and pump is $5000; the installed cost of the motor to drive the pump is $300; the salvage value of the system in 10 years is $600; and the energy cost per hour of operation is $0.20. The pump will have to be rebuilt at the end of year 5 at a cost of $400.

a) On the basis of a 10 year life, find the number of hours of operation per year for which the cost of the two proposed systems will be equal if the interest rate is 9%.

b) Which proposal is preferred if the number of hours of operation per year is greater than the number of hours of operation calculated in Problem 7a?