A metal fabrication shop has a single punch press. There are currently three parts that the shop has agreed to produce that require the press, and it appears that they will be supplying these parts well into the future. You may assume that the press is the critical resource for these parts, so that we need not worry about the interaction of the press with the other machines in the shop. The relevant information here is Part Annual Contracted Cost Production Number Amount (demand) Setup Cost (per unit) Rate (per year)

1 2,500 $80 $16 45,000 2 5,500 120 18 40,000 3 1,450 60 22 26,000 Holding costs are based on an 18 percent annual interest rate, and the products are to be produced in sequence on a rotation cycle. Setup times can be considered negligible.

a. What is the optimal time between setups for part number 1?

b. What percentage of the time is the punch press idle, assuming an optimal rotation cycle policy?

c. What are the optimal lot sizes of each part put through the press at an optimal solution?

d. What is the total annual cost of holding and setup for these items on the punch press, assuming an optimal rotation cycle?