Danny Steel, Inc., fabricates various products from two basic inputs, bar stock and sheet stock. Bar

stock is used at a steady rate of $1,000$ units per year and costs $$200$ per bar. Sheet stock is used at a

rate of $500$ units per year and costs $$150$ per sheet. The company uses a $20\%$ annual holding cost

rate, and the fixed cost to place an order is $$50,$ of which $$10$ is the cost of placing the purchase order

and $$40$ is the fixed cost of a truck delivery. The variable $($i$.$e$.,$ per unit charge$)$ trucking cost is

included in the unit price. The plant runs $365$ days per year.

$($a$)$ Use the EOQ formula with the full fixed order cost of $$50$ to compute the optimal order quantities,

order intervals, and annual cost for bar stock and sheet stock. What fraction of the total annual

$($holding plus order$)$ cost consists of fixed trucking cost?

$($b$)$ Using a week $($seven days$)$ as the base interval, round the order intervals for bar stock and sheet

stock to the nearest power of $2.$ If you charge the fixed trucking fee only once for deliveries that

coincide, what is the annual cost now?

a$)$ Determine the optimal number of bolts for the plant to purchase and the time between placements of orders.

b$)$ What is the yearly holding and setup cost for this item?

c$)$ Suppose instead of small bolts we were talking about a bulky item, such as packaging materials. What problem might there be with our analysis?