the optimal ordering strategy , statistics homework help

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1. A local company sells many varieties of shoes. For one particular line, the company buys the shoes for $15.00 and sells them for $30.00. The cost of placing an order for the shoes is $50.00, and it takes a week before the shoes arrive. Annual demand for the shoes is approximately normally distributed with a mean of 5,200 pairs and a standard deviation of 520 pairs. The cost for holding shoes in inventory is $.12 per dollar value per year. If shoes are out of stock, the goodwill cost is estimated to be $5.00 per pair, and the sale is lost. Find the optimal ordering policy for the shoe company. (12) 2. Daniel Baker owns a shop that sells special car batteries. He uses a monthly periodic review order policy, and sets a 95% service level. During a four-week period, demand for batteries is approximately normally distributed with a mean of 200 and a standard deviation of 40. His lead time is two (2) weeks. If his current inventory is 42 batteries on the day of review, how many batteries should he order? (12) 3. See the following Management Scientist output. In this problem, we are trying to determine the optimal number of rolls of four types of fabric (1, 2, 3, and 4) to produce. Note that the third constraint concerns the available quantity of a certain chemical resin used for each type of fabric, the fourth constraint concerns the available quantity of polyester, and the final two constraints are imposed to ensure that we will incur a $200 penalty if we produce at least 600 units of Types 2 and 4 (since this will require us to redeploy an additional production line). A. Which constraints are binding? Explain. (2) B. Which constraint would we prefer to see relaxed? Explain. (3) C. Nora in Accounting realized that the profit associated with Type 1 fabric should be $8.00/unit. What effect would this have on the optimal solution? (3) D. If the availability of the chemical (third constraint) were 15,000, what effect would this have? (3) LINEAR PROGRAMMING PROBLEM MAX 6X1+7X2+4X3+7X4-200X5 S.T. 1) 2) 3) 4) 5) 6) 1X1+1X2+1X320 4X1+4X2+3X3+3X4
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Explanation & Answer

Kindly see attached file with the step by step solution to the three problems.

1. A local company sells many varieties of shoes. For one particular line, the
company buys the shoes for $15.00 and sells them for $30.00. The cost of placing
an order for the shoes is $50.00, and it takes a week before the shoes arrive.
Annual demand for the shoes is approximately normally distributed with a mean
of 5,200 pairs and a standard deviation of 520 pairs. The cost for holding shoes in
inventory is $.12 per dollar value per year. If shoes are out of stock, the goodwill
cost is estimated to be $5.00 per pair, and the sale is lost. Find the optimal
ordering policy for the shoe company. (12)
DATA:
• Buying price = $15/unit
• Selling price = $30/unit
• Order cost = $50
• Lead time = 1 week
• Annual demand = 5200 units
• Standard deviation for annual demand = 520
• Annual holding cost = $0.12/unit
• Stock out cost = $5/unit
CALCULATIONS:
To evaluate which is the optimal ordering strategy of the company we need to estimate:
Economic order quantity
Target service level
Restock level

-

These variables are calculated below:
Estimation of the economic order quantity:

𝐸𝑂𝑄 =...


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