2-25. A design engineer must select the horsepower for a motor to drive a pump. Horsepower rating is a continuous design parameter with values in the range of 10 to 40 horsepower. The motor will have an annual ownership cost of $120 plus $0.60 per horsepower. The operating costs of such motors for 1 horsepower-hour will be $0.055 divided by the horsepower rating. Nine thousand horsepower-hours will be needed per year. (2.3)

a. Determine what horsepower should be specified for a minimum total annual cost.

b. Show that you have minimized total cost per year.