A print shop plans to maintain 5 different presses, replacing each every few years on a regular cycle. The following table shows the replacement cost (in thousands of dollars) of each press, and the estimated annual income (in thousands of dollars)

that each can generate when new. However, as the presses grow older, their productivity declines;

final values in the table show the (simple, not compound)

percent income loss each year of life.

Press 1 2 3 4 5 Replace 110 450 150 675 320 Income 90 110 55 220 250 Decline 5% 20% 30% 20% 40%

The owner wishes to choose a replacement (cycle)

time for each press that minimizes total replacement and lost income costs within the $250,000 she can average annually for purchasing new presses.

(a) Formulate this replacement problem as a constrained NLP. (Hint: What is the average income loss on press j as a function of the replacement time for j?)

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