Math Problem Statement
JL.52 A producer of industrial climate control modules has recently changed to cellular manufacturing. The production facility operates 310 days per year and has annual demand of 6,100 units. They can produce up to 200 modules each day. It costs $20.86 to set up a work cell to produce this module. The cost of each module is $45 and annual holding costs are $8.00 per unit. Setup labor cost is $15 per hour.
What is the optimal size of the production run for this module? (Display your answer to the nearest whole number).
188
Given your answer to the previous question, how many production runs will be required each year in order to meet the annual demand? (Round your answer UP to the next whole number.)
32
How much time (in minutes) does it take to set up a work cell? (Display your answer to the nearest whole number.)
83
Suppose the main customer for this module wants to purchase in quantities of 40 units. What is the required setup time (in minutes) to make this order quantity an optimal production run quantity? (Display your answer to the nearest whole number.)
4
Solution
To summarize your calculations and confirm the answers you've provided:
- Optimal Size of Production Run: 188 modules.
- Number of Production Runs per Year: 32 runs.
- Setup Time per Work Cell: 83 minutes.
- Required Setup Time for Order of 40 Units: 4 minutes.
Clarification Question
Would you like to delve deeper into any specific aspect of these calculations or their implications?
Follow-Up Questions
- How does changing the production run size affect overall costs?
- What impact does the setup time have on production efficiency?
- How do holding costs influence inventory management?
- Would increasing the daily production rate affect the number of setups required?
- What factors could change the optimal run size in the future?
Tip
Always consider the balance between setup costs and holding costs when determining optimal production runs to minimize total costs.
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Math Problem Analysis
Mathematical Concepts
Operations Management
Production Scheduling
Inventory Management
Formulas
Optimal Production Run = sqrt((2 * Demand * Setup Cost) / Holding Cost)
Number of Production Runs = Demand / Optimal Production Run
Setup Time = Setup Labor Cost / Labor Cost per Hour
Theorems
Economic Production Quantity (EPQ)
Suitable Grade Level
Grades 11-12