Question

A metal fabrication shop has a single punch press. There are currently three partsthat the shop has agreed to produce that require the press, and it appears that theywill be supplying these parts well into the future. You may assume that the press isthe 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 Number Demand/year Set up Cost ($) Cost per Unit Production rate/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. What is the optimal cycle time in years?

Answer 1

The optimal cycle time for a metal fabrication shop with three different parts can be determined by finding the greatest common divisor (GCD) of the production rates. In this case, the GCD is 100 years.

Step-by-step explanation:

The optimal cycle time for the metal fabrication shop to produce the parts is determined by the part with the lowest cycle time. The cycle time is the production rate in years. In this case, the production rates for the three parts are 45,000 units/year, 40,000 units/year, and 26,000 units/year respectively. To determine the optimal cycle time, we need to find the greatest common divisor (GCD) of the production rates.

1. Part 1: 45,000 = 3 * 3 * 5 * 5 * 5 * 5 * 2 * 2 * 3 * 3 * 3 / 1
2. Part 2: 40,000 = 2 * 2 * 2 * 2 * 2 * 5 * 5 * 5 * 5 / 1
3. Part 3: 26,000 = 2 * 2 * 2 * 5 * 5 * 13 / 1

The GCD of the three production rates is the product of the common factors raised to their lowest power, which in this case is 2 * 2 * 5 * 5 = 100. Therefore, the optimal cycle time is 100 years.