A machinist will remove excess metal from a rotary (round) machine part by passing the cutting tool of a lathe along 42 inches of the part length. For a lathe turning at N revolutions per minute and advancing the tool at a feed rate of f inches per revolution, classic empirical relationships project the effective life of a cutting tool

(in minutes) at tool life = a 5

Nf 0.60 b 6.667 Each time a tool wears out the operator must install a new one and spend 0.1 hour realigning the machine. Engineers wish to choose the machining plan that minimizes total cost at $52 per hour for machinist time and $87 each for new tools. Speed N must be in the interval [200, 600] and feed rate f in the interval [0.001, 0.005].

(a) Formulate this machining problem as a constrained NLP.

(b) Use class optimization software to start from a feasible solution and compute at least a local optimum.