Brett's Gift Box estimates that it will sell 30,000 porcelain figurines next year.Because porcelain figurines are so easily damaged,the average per unit carrying cost of the figurines is $25.The per order cost of ordering is $800.Assume that Brett wants a safety stock of 75 figurines.If Brett reorders the figurines based on the economic order quantity,what is Brett's average inventory of porcelain figurines?

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The Economic Order Quantity (EOQ) model is used to minimize the total inventory costs, which include ordering costs and carrying costs. The EOQ formula is given by $\sqrt{(2DS)/H}$, where $D$ is the demand, $S$ is the ordering cost per order, and $H$ is the carrying cost per unit per year.Given:- $D = 30,000$ figurines- $S = $800$- $H = $25$First, calculate the EOQ:$$EOQ = \sqrt{\frac{(2*30000*800)}{25}} = \sqrt{1920000} = 1385.64$$The average inventory is half the EOQ plus the safety stock:$$Average\ Inventory = \frac{EOQ}{2} + Safety\ Stock = \frac{1385.64}{2} + 75 = 692.82 + 75 = 767.82$$Rounding to the nearest whole number gives an average inventory of approximately 768 figurines.

Brett's Gift Box Estimates That It Will Sell 30,000 Porcelain