The university motor pool3 provides a large number of cars n for faculty and staff traveling on university business. Motor pool cars have an average annual cost of f dollars per car for fixed expenses such as depreciation, insurance, and licensing, plus a variable operating cost of vm cents per mile driven. Those travelers who cannot be accommodated by the pool must drive their personal cars and be reimbursed at vp cents per mile.

Demand varies greatly among times of the year, but an extensive analysis of past travel records has fitted regression equations m1n2!am + bmn + cm>n p1n2!ap + bpn + cp>n to the annual numbers of miles that would be driven in motor pool and personal cars as a function of the size of the motor pool available. Formulate a 1-variable unconstrained NLP to compute a minimum total cost motor pool size. Ignore integrality.