Question

Demand for cones of organic wool at a SmartWool sock factory is constant at 640 units PER MONTH. SmartWool purchases the cones from its supplier for a cost of $32 per unit and incurs a fixed order cost of $2380 each time it places an order regardless of the number of units ordered. The holding cost per unit per year at the factory is 42% of the per unit purchase cost. The lead time to receive the order is 5 days. Assume SmartWool operates 364 days, 52 weeks, or 12 months per year.

Calculate the optimal order quantity for SmartWool.

Answer Choices:

a.476.1

b.824.6

c.1368.87

d.22.2

e.9329.5

f.1649.2

g.3842.7

Answer 1

The optimal order quantity for SmartWool is calculated using the EOQ formula. SmartWool's annual demand, fixed order cost, and holding cost percentage are used to calculate this figure, which is 'f', 1649.2 units.

Step-by-step explanation:

The student's question pertains to the calculation of the optimal order quantity for SmartWool, a company that purchases organic wool. To calculate the optimal order quantity, we use the Economic Order Quantity (EOQ) formula:

EOQ = √((2DS)/H)

where:
D = Demand rate (units per period)
S = Order cost (per order)
H = Holding cost (per unit per period)

The demand (D) is given as 640 units per month. The order cost (S) is $2380, and the holding cost (H) is 42% of the unit cost, thus H = 0.42 * $32 = $13.44 per unit per year. Considering SmartWool operates 364 days a year, we will convert the monthly demand to a yearly demand by multiplying it by 12. The formula then becomes:

EOQ = √((2 * 640 * 12 * $2380)/$13.44) = √1649.2

The correct answer for the optimal order quantity for SmartWool is 'f', which corresponds to 1649.2 units.