# ======== A distributor is planning to calculate the optimal service level given the following information. Based on past data, sales response rate…

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 ΔP

ΔP =    Trading Margin x Sales Response Rate x Annual Sales

=\$18 x 0.12% x120,000

=\$2,592

® Therefore, Delta_P (ΔP) is \$2592

b. Calculate ΔC

ΔC =   Annual Carrying cost x Standard Product Cost X Demand Standard Deviation x lead – time x ΔZ

= 24% x \$75 x 300 x 4 x ΔZ

= 21600ΔZ

® Therefore, Delta_C (ΔC) is 21600ΔZ

c. Calculate ΔZ

Set ΔP = ΔC

ΔZ = (ΔP / ΔC)

= 2592 / 21600

= 0.12

® Therefore, ΔZ is 0.12

d. Determine the optimal service level

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