Tomlinson Furniture has a single lathe for turning the wood for various furniturepieces, including bedposts, rounded table legs, and other items. Four forms areturned on the lathe and produced in lots for inventory.To simplify scheduling, one lotof 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 ProductionPiece Requirements Time (hours) Cost Rate (units/day)J–55R 125 1.2 $20 140H–223 140 0.8 35 220K–18R 45 2.2 12 100Z–344 240 3.1 45 165Worker time for setups is valued at $85 per hour, and holding costs are based ona 20 percent annual interest charge. Assume 20 working days per month and12 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 itis not used for any other purpose?d. Draw a graph showing the change in the inventory level over a typical cycle foreach product.e. Discuss why the solution you obtained might not be feasible for the firm, or whyit might not be desirable even when it is feasible.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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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 Production
Piece Requirements Time (hours) Cost 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.

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