Problem 2.1 Demand for T-shirts is normally distributed with mean 1,000 and standard deviation 200. Cost of one T-shirt is $10, the selling price of one T-shirt is $15, each unsold T-shirt is worth $8. 1. What is the under-stocking cost Cu?

Under-stocking cost (Cu) = Price Cost = 15 10 = $5

2. What is the over-stocking cost Co?

Overstocking Cost (Co) = Cost Salvage = 10 8 = $2

3. What is the optimal initial order quantity if the demand is given by N(1,000 , 200²)?

Optimal Order Quantity: Critical Ratio = Cu/(Cu + Co) = 5/(5 + 2) = 5/7 = 0.714286 For 0.714286, z = 0.565948822 Quantity = mean + z*Standard Deviation Mean = 1000 Standard Deviation =200² Order Quantity = 1000 + 0.565948822*200² = 23637.95288

Suppose we have the second ordering opportunity when the demand exceeds our initial order. The second order prevents lost sales, because we can simply choose a second order quantity to ensure that all demand is satisfied. However, we need to pay an extra 20 percent premium over the regular price for those T-shirt purchased from the second order. Given this new opportunity, 4. What is the under-stocking cost Cu for the initial ordering decisin?

5. What is the over-stocking cost Co for the initial ordering decision?

6. What is the optimal initial order quantity if the demand is given by N(1,000 , 200²)?

please solve the problems 4,5,6.( and be careful of the numers 200²⁾