(5) Alpha Assemblies produces a wide variety of products in their central Nebraska facility. Many of these products fit within a line of standard truck and trailer parts. Within this is a set of hitches that can be made in two sizes (1-1/4 and 2) and five models (light duty, medium duty, medium duty with extender, heavy duty, and heavy duty with extender). All of the hitches in this line have "natural" finishes so no additional steps are necessary after they are cast. The machine used to cast these ten hitch variations is available for 2000 hours per year (40 hours per week for 50 weeks). Operators are paid $15.00 per hour including benefits.

Hitch J is the 2 inch, heavy duty with extender, natural hitch.

After discussions with the production manager, Simone has come to realize that her assumption on EOQ is not appropriate. Since EOQ is designed for situations where all of the inventory shows up all at once, which would often be the case for a purchased items and in some cases for manufactured items when everything must move forward as a full batch, and the situation here is that each item may move into inventory as soon as it comes out of production (without waiting for the other items) EOQ with gradual deliveries (sometimes called Economic Run Length (ERL) or Economic Production Quantity (EPQ), among other things) would be more appropriate.

The forecast annual demand for next year of Hitch J is 20,661 and the current batch size is 2,390 units. It takes 0.049 hours to produce each Hitch J. The setup time is 6.7 hours per setup conducted by a single operator with no other setup costs incurred. The holding cost is $1.77 per unit per year. Production and demand both occur 250 days per year. The facility operates 8 hours per day.

First, determine the recommended batch size using EOQ with Gradual Deliveries (ERL, EPQ) and then determine how many days of idle time will be available between producing a batch and when it will be time to produce the next batch. Simply, if it takes x days to produce a batch and y days to sell the batch, the difference is the time that you are just selling but not producing. This time would then be available to produce a different hitch.

Don't round any numbers in the middle of the problem. Provide your answer to two (2) decimal places.