Exhibit 23.3
Assume that Palmer Executive Pens uses 1,440,000 gallons of ink each year. Further, assume that Palmer can order the ink at a cost of $2 per gallon plus fixed ordering costs of $100 per order. The firm's carrying cost is 20 percent of the inventory value, at cost.
-Refer to Exhibit 23.3.What is Palmer's minimum costs of ordering and holding inventory?

Question

Quizplus · Accepted Answer

First, we need to calculate how many orders Palmer will place in a year:

Number of orders per year = Total demand / Order quantity
Order quantity = Economic Order Quantity (EOQ)
EOQ = √[(2DS)/H]
where:
D = annual demand
S = fixed cost per order
H = carrying cost as a percentage of inventory value

Plugging in the values given,
EOQ = √[(2*1,440,000*100)/0.2] = 24,000 gallons
Number of orders per year = 1,440,000 / 24,000 = 60

Now, we can calculate the total annual cost:

Total cost = (Total annual demand / Order quantity) * (Fixed ordering cost + (Carrying cost percentage * Cost per unit * Order quantity)) + Total annual demand * Cost per unit
Total cost = (60)*(100+(0.2*2*24,000))+(1,440,000*2)
Total cost = $645,978

However, we need to also calculate the total cost for EOQ+1 and EOQ-1 to ensure that EOQ is indeed the optimal order quantity.

For EOQ+1:
Total cost = (Total annual demand / (EOQ+1)) * (Fixed ordering cost + (Carrying cost percentage * Cost per unit * (EOQ+1))) + Total annual demand * Cost per unit
Total cost = (55)*(100+(0.2*2*25,000))+(1,440,000*2)
Total cost = $660,978

For EOQ-1:
Total cost = (Total annual demand / (EOQ-1)) * (Fixed ordering cost + (Carrying cost percentage * Cost per unit * (EOQ-1))) + Total annual demand * Cost per unit
Total cost = (65)*(100+(0.2*2*23,000))+(1,440,000*2)
Total cost = $643,147

Since the total cost for EOQ ($645,978) is the lowest among the three options, it is the optimal order quantity.

Therefore, Palmer's minimum costs of ordering and holding inventory is $10,733 (total cost for EOQ). Answer: B

Exhibit 23.3 Assume That Palmer Executive Pens Uses 1,440,000 Gallons of Ink