Answered>Order 6778

Need help on answer to letter D at bottom:

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A distributor is planning to calculate the optimal service level given the following information. Based on past data, sales response rate is 0.12% change in revenue for a 1% change in the service level (fill rate). Trading margin is $18 per item, inventory carrying cost is 24% per year, annual sales through the warehouse is 120,000 items. Cost of each item is $75, demand standard deviation is 300 items for a week, and the lead time is 4 weeks.

a. Calculate ?P 

?P =    Trading Margin x Sales Response Rate x Annual Sales

            =$18 x 0.12% x120,000

            =$2,592

® Therefore, Delta_P (?P) is $2592

b. Calculate ?C 

?C =   Annual Carrying cost x Standard Product Cost X Demand Standard Deviation x lead – time x ?Z

            = 24% x $75 x 300 x 4 x ?Z

            = 21600?Z

® Therefore, Delta_C (?C) is 21600?Z

c. Calculate ?Z 

Set ?P = ?C

?Z = (?P / ?C)

            = 2592 / 21600

            = 0.12

® Therefore, ?Z is 0.12

d. Determine the optimal service level