A design engineer is sizing a transfer pump motor. The size of the motor is a continuous variable between $10$ and $40$ kW$.$ The transfer pump will be required to supply $9,000$ kWh of work per year.

The annual ownership cost of the pump is given by: CF $+$ cown$*$P$,$ where CF is the fixed cost of the pump, cown is the incremental ownership cost per kW$,$ and P is the power rating of the motor in kilowatts.

The operating cost of the motor per kWh will be given by: Cop$=$ cv$/$P$,$ where Cop is the operating cost per kWh$,$ and cv is the incremental operating cost constant.

Create and solve a model of this problem using the following parameter values: CF $=$ $$120,$ cown $=$ $$0\mathrm{.}60,$ and cv $=$ $$0\mathrm{.}055.$ The model should determine the optimal size motor for this application.