Quarter-inch stainless-steel bolts, 1.5 inches long are consumed in a factory at a fairly steady rate of 60 per week. The bolts cost the plant 2 cents each. It costs the plant $12 to initiate an order, and holding costs are based on an annual interest rate of 25 percent.

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

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

1) the number of weeks per year = 52 weeks

Average weekly demand (d) = 60 per weeks

Annual demand (D) = d x number of weeks per year = 60 x 52 = 3120 bolts

Ordering cost (O) = $12

Cost per bolt = 2 cents = $0.02

Holding cost (H) = 25% of cost = 0.25 * $0.02 = $0.005

a) Optimal order quantity (Q) = √ (2DO/H)

= √[ (2 X 3120 X 12) / 0.005]

= √ (74880/0.005)

= √14976000

= 3870 bolts

Time between orders = (Q/D) number of weeks per year

= (3870/3120) 52

= 64.5 or 65 weeks

b) Annual holding cost = (Q/2) H = (3870/2) * 0.005 = $9.675

Annual setup cost = (D/Q) * O = (3120/3870) * 12 = $9.674