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# Quantitative Analysis (Decision Methods)

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I got these problems wrong on a recent quiz...& I need thorough explanation and solution(s); so that I can use for reference in studying for the final examination. I'm really not understanding the logic & thought processes.

Thank you.

(See attached file for full problem description)

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1. ArtOrgan, Ltd. distributes replacement units for human mitral heart valves. Their forecast sales, at a price of \$7,900 per unit, is 12,500 units. ArtOrgan's cost is \$5,900 per unit. The cost of ordering is \$75 per order and the average carrying cost per unit per year works out to be about 5% of the cost of the valve. Lead time is 4 working days. Determine, based on 250 working days per year:

(a) the economic order quantity
(b) the optimal number of orders per year
(c) the reorder point

If demand variability during lead time is normally distributed with a standard deviation equal to 10% of the mean:

(d) what percentage of the order cycles will result in at least one stockout?
(e) what amount of safety stock would be required to provide 95% coverage?

2. As a supervisor of a production department, you must decide the daily production totals of a certain product that has two models, the deluxe and the special. The profit on the deluxe model is \$12 per unit, and the special's profit is \$10. Each model goes through two phases in the production process, and there are only 100 labor-hours available daily at the construction stage and only 80 labor-hours available at the finishing and inspection stage. Each deluxe model requires 20 minutes of construction time and 10 minutes of finishing and inspection time. Each special model requires 15 minutes of construction time and 15 minutes of finishing and inspection time. The company has also decided that the special model must comprise at most 60 percent of the production total.

(a) What is the best production strategy?
(b) What is the profit from the best strategy?
(c) If another worker is hired, to which department would you assign him?
Why?

How would your answers to (a) and (b) be affected if you discovered that the "specials" could only be sold by cutting their profit contribution to \$8?

(d) before your production plan was established and executed?
(e) after your production plan was established and executed?
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(See attached file for full problem description)