Tomlinson Furniture has a single lathe for turning the wood for various furniture pieces, including bedposts, rounded table legs, and other items. Four forms are turned on the lathe and produced in lots for inventory. To simplify scheduling, one lot of each type will be produced in a cycle, which may include idle time. The four products and the relevant information concerning them appears in the following table. Monthly Setup Unit Piece Requirements Time (hours) Cost Production Rate (units/day) J-55R 125 1.2 $20 140 H-223 140 0.8 35 220 K-18R 45 2.2 12 100 Z-344 240 3.1 45 165 Worker time for setups is valued at $85 per hour, and holding costs are based on a 20 percent annual interest charge. Assume 20 working days per month and 12 months per year for your calculations. a. Determine the optimal length of the rotation cycle. b. What are the optimal lot sizes for each product? c. What are the percentages of uptime and downtime for the lathe, assuming that it is not used for any other purpose? d. Draw a graph showing the change in the inventory level over a typical cycle for each product. e. Discuss why the solution you obtained might not be feasible for the firm or why it might not be desirable even when it is feasible.