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

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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