Question

A store owner purchases boxes of cereal for a price of $3.65 each and sells 4 box of cereal per week. The widgets are offered in cases of 48 each (no partial case shipments are allowed). The retailer's cost of holding one widget in inventory for one year is $0.83. When the retailer purchases widgets, there is a fixed charge of $74 for each order.

How many cases of widgets should the retailer purchase at one time?

Answer 1

The question is aimed at determining the optimal number of cases of widgets a retailer should order using the Economic Order Quantity (EOQ) model, considering annual demand, fixed order costs, and holding costs.

Step-by-step explanation:

The question involves calculating the optimal number of cases of widgets the retailer should purchase at one time, which involves understanding concepts such as inventory costs, fixed order costs, and sales velocity. To arrive at the solution, the Economic Order Quantity (EOQ) model can be applied, which is a formula used to determine the ideal order quantity a company should purchase to minimize its inventory costs such as holding costs, shortage costs, and order costs.

The EOQ formula is given by the square root of (2DS/H), where D is the annual demand, S is the order cost, and H is the holding cost per unit per year.

Given the retailer sells 4 boxes of cereal per week, the annual demand (D) is 4 boxes × 52 weeks = 208 boxes per year. The fixed order cost (S) is given as $74 per order, and the holding cost (H) is $0.83 per widget per year. Cases contain 48 widgets each, so we need to calculate how many cases to order each time. This requires dividing the EOQ by the number of widgets per case after we calculate the EOQ.