# Ebb&Flow (E&F) sells yoga supplies including their popular​ eco-friendly yoga mat design. The monthly demand for yoga mats follows a normal distribution with mean 540 mats per month and standard deviation 56 systems per month.​ E&F reviews its inventory every 24 days. It takes 18 days to receive an order delivery​ (assume 30 days per​ month). E&F would like to maintain a service level of 93​%. E&F purchases the systems from a supplier for \$35 per system. Annual holding cost is 20​% of the purchase cost per audio system. You may use the following table of values for the Standard Normal distribution to find your z value. Z: 2.326; 2.054; 1.881; 1.751; 1.645; 1.555; 1.476; 1.405; 1.341; 1.282 P(Z<=z): .99; .98; .97; .96; .95; .94; .93; .92; .91; .9 a) Compute the safety stock level you recommend for​E&F. b) Compute average inventory on order ​c) Compute the annual holding cost for carrying the safety stock ​(round your response to nearest​cent).

a. P = interview review duration = 24 days = 24/30 = 0.8 Months; L = Lead time = 18days = 18/30 = 0.6 Months;

σd = 56

So, σP+L = σd * Sqrt(P+L) = 56*Sqrt(1.4) = 66.26 Units.

For 93% service level, Z = 1.476 ( As seen from the table)

Therefore, Safety stock = Z* σP+L = 1.476*66.26 = 97.79 or 98 Units

b. Average inventory on order = Average demand during the P+L interval + Safety stock = (1.4*540) + 98 = 854 Mats

c. Total cost of the safety stock = \$35 * 98 = \$ 3430

Therefore, Annual Holding cost of the safety stock = 20% of 3430 = \$ 686

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