(a) Assume that all ingredients are ordered independently. For each ingredient, determine the optimal cycle time and order quantity. Calculate the associated total cost of all ingredients. (b) Assume that all ingredients are ordered independently, and the cafeteria management wants to limit their annual inventory holding cost by $52.5. Using Lagrange multiplier technique, determine the optimal cycle time and order quantity for each ingredient. Calculate the associated total cost of all ingredients. (c) Assume that all ingredients have a fixed (common) order cycle. Determine the optimal cycle time, the order quantity for each ingredient, and the associated total cost. Draw a figure that illustrates the change in inventory levels of the ingredients.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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4.
The FCC Cafeteria, a fast lunch spot in Çankaya University campus, purchases several basic cooking
ingredients from a supplier. The annual usage (demand), purchasing cost, and setup (order) cost of these
ingredients are given in the table below. The inventory carrying rate is 0.10 per unit per year.
Ingredient
Annual Demand (in units)
Purchasing Cost ($ / unit)
Setup Cost ($ / order)
1
3
4
100
100
200
100
10
40
10
10
2
2
4
3
(a) Assume that all ingredients are ordered independently. For each ingredient, determine the optimal
cycle time and order quantity. Calculate the associated total cost of all ingredients.
(b) Assume that all ingredients are ordered independently, and the cafeteria management wants to limit
their annual inventory holding cost by $52.5. Using Lagrange multiplier technique, determine the
optimal cycle time and order quantity for each ingredient. Calculate the associated total cost of all
ingredients.
(c) Assume that all ingredients have a fixed (common) order cycle. Determine the optimal cycle time, the
order quantity for each ingredient, and the associated total cost. Draw a figure that illustrates the
change in inventory levels of the ingredients.
Transcribed Image Text:4. The FCC Cafeteria, a fast lunch spot in Çankaya University campus, purchases several basic cooking ingredients from a supplier. The annual usage (demand), purchasing cost, and setup (order) cost of these ingredients are given in the table below. The inventory carrying rate is 0.10 per unit per year. Ingredient Annual Demand (in units) Purchasing Cost ($ / unit) Setup Cost ($ / order) 1 3 4 100 100 200 100 10 40 10 10 2 2 4 3 (a) Assume that all ingredients are ordered independently. For each ingredient, determine the optimal cycle time and order quantity. Calculate the associated total cost of all ingredients. (b) Assume that all ingredients are ordered independently, and the cafeteria management wants to limit their annual inventory holding cost by $52.5. Using Lagrange multiplier technique, determine the optimal cycle time and order quantity for each ingredient. Calculate the associated total cost of all ingredients. (c) Assume that all ingredients have a fixed (common) order cycle. Determine the optimal cycle time, the order quantity for each ingredient, and the associated total cost. Draw a figure that illustrates the change in inventory levels of the ingredients.
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