Question

OPRE. 3310: Homework Assignment 3

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Betty bakes and sells bagels all year round. Betty has to plan and manage inventories of paper take-out bags with her logo printed on them to satisfy customer demand. Daily demand for take-out bags is normally distributed with a mean of 90 bags and a standard deviation of 30 bags. Betty's printer charges her $10 per order for print setup independent of order size. Bags are printed at 5 cents ($0.05) each bag. It takes 4 days for an order to be printed and delivered. The annual inventory holding cost is $0.0125 per bag. Assume 360 days per year.

What is the optimal order quantity per order for Betty?

Answer 1

The question pertains to finding the optimal order quantity for Betty's bagel shop using the Economic Order Quantity (EOQ) formula, which involves the annual demand, ordering costs, and holding costs.

Step-by-step explanation:

To determine the optimal order quantity for Betty's bagel shop, we need to use the Economic Order Quantity (EOQ) model. The EOQ model calculates the ideal order size to minimize the sum of ordering costs, holding costs, and stock out costs. In this case, we are provided with ordering costs ($10 per order plus $0.05 per bag), holding costs ($0.0125 per bag per year), and the annual demand based on the daily demand multiplied by 360 days.

The formula for EOQ is: EOQ = √((2 x Demand x Ordering Cost) / Holding Cost). The Demand is the daily demand of 90 bags multiplied by 360 days to give the annual demand. The Ordering Cost is the setup cost of $10 per order, and the Holding Cost is the annual holding cost per bag of $0.0125.

When we plug in the values, we get: EOQ = √((2 x 90 x 360 x $10) / $0.0125) = √((648,000) / $0.0125), which we then calculate to find the EOQ that minimizes Betty's costs associated with ordering and holding the take-out bags.