7. A steel rolling mill can produce I-beams at the rate of 20 tons per week. Customer demand for the beams is 5 tons per week. To produce I-beams, the mill must go through a setup that requires changing to the appropriate rolling patterns. Each setup costs the mill $10,000 in labor and lost produc- tion. I-beams cost the mill $2,000 per ton and the mill has a holding cost of 25 percent. What is the optimal production batch size for I-beams? What is the annual setup cost of the optimal policy? What is the annual holding cost? E
7. A steel rolling mill can produce I-beams at the rate of 20 tons per week. Customer demand for the beams is 5 tons per week. To produce I-beams, the mill must go through a setup that requires changing to the appropriate rolling patterns. Each setup costs the mill $10,000 in labor and lost produc- tion. I-beams cost the mill $2,000 per ton and the mill has a holding cost of 25 percent. What is the optimal production batch size for I-beams? What is the annual setup cost of the optimal policy? What is the annual holding cost? E
Chapter1: Financial Statements And Business Decisions
Section: Chapter Questions
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How do I do question 7?
Transcribed Image Text:**Problem 7: Production and Cost Analysis of I-Beams**
A steel rolling mill has the capability to produce I-beams at a rate of 20 tons per week. The customer demand for these beams is 5 tons per week. In order to produce I-beams, the mill undergoes a setup process, which involves altering the rolling patterns, and incurs a cost of $10,000 for labor and lost production per setup. The cost of producing I-beams is $2,000 per ton, and the mill has a holding cost of 25%.
**Questions:**
- What is the optimal production batch size for I-beams?
- What is the annual setup cost based on this optimal policy?
- What is the annual holding cost?
**Considerations:**
- The mill's production capability surpasses the demand, suggesting an inventory model to determine the optimal batch size and associated costs.
- Setup costs and holding costs need to be balanced to minimize total production and inventory costs.
This analysis requires understanding of economic production quantity (EPQ) models and can involve calculations such as determining the EPQ, total cost minimization, and annual cost evaluations.
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