A steel workpiece is to be cut9 in a lathe to a target depth of 0.04 inch. Empirical studies with this type of steel express the properties of the resulting product as finish !0.41n3.97f 3.46d0.91 power !nf 0.75d0.90 time !nf where v is the cutting speed in revolutions per minute, f is the feed rate in inches per revolution, and d is the depth of cut in inches. Finish variation must be kept no greater than 150, required power no more that 4.0, cutting speed between 285 and 680, and feed rate between 0.0075 and 0.0104. Within these limits, the first priority goal is to make the depth of cut as close as possible to 0.04 inch, and the second is to complete the cut in at most time 1.5 (minutes).

(a) Formulate a preemptive goal NLP to choose cutting parameters.

(b) Enter and (at least locally) solve your goal program using class optimization software.