Question

Henry Crouch’s law office has traditionally ordered ink refills 60 units at a time. The firm estimates that carrying cost is 40% of the $10 unit cost and that annual demand is about 240 units per year. The assumptions of the basic EOQ model are thought to apply.

For what value of ordering cost would its action be optimal?

Answer 1

The value of the ordering cost for which Henry Crouch's law office action of ordering ink refills 60 units at a time would be optimal is $5 per order according to the EOQ model.

Step-by-step explanation:

The student's question concerns economic order quantity (EOQ) which is a principle within the field of business operations and inventory management. According to the EOQ model, Henry Crouch's law office wants to find the ordering cost that would make their action of ordering 60 units at a time optimal.

The EOQ formula is given by:

EOQ = √((2DS)/H)

where:

• D is the annual demand (240 units)
• S is the ordering cost per order
• H is the holding or carrying cost per unit per year (40% of the $10 unit cost = $4)

Given that the firm is already ordering optimally at 60 units, we can rearrange the formula to solve for S (ordering cost):

S = (EOQ^2 * H) / (2D)

Plugging in the known values:

S = (60^2 * 4) / (2 * 240) = 2400 / 480 = $5

So, the ordering cost for which the law office's action would be optimal is $5 per order.

Answer 2

The optimal ordering cost for Henry Crouch's law office, which orders 60 units of ink refills at a time and has an annual demand of 240 units with a carrying cost of 40% of the $10 unit cost, is $30.

Step-by-step explanation:

The student is asking to find the value of the ordering cost for which the current action to order 60 units at a time is optimal based on the Economic Order Quantity (EOQ) model. We are given the carrying cost as 40% of the unit cost, which is $10, and the annual demand is 240 units. The EOQ formula is EOQ = sqrt((2DS)/H), where D is the annual demand, S is the ordering cost per order, and H is the annual holding (or carrying) cost per unit.

To find the value of S where ordering 60 units is optimal, we will set EOQ to 60 units and solve for S. Since we have H as 40% of $10, which is $4, and D as 240 units, we would have:

• EOQ = 60 = sqrt((2*240*S)/4)
• 3600 = (480*S)/4
• 3600 * 4 = 480 * S
• 14400 = 480 * S
• S = 14400 / 480
• S = $30

Therefore, if the ordering cost is $30, ordering 60 units at a time would be optimal under the basic EOQ model assumptions.