Question

IM.84 An outdoor equipment manufacturer sells a rugged water bottle to complement its product line. They sell this item to a variety of sporting goods stores and other retailers. The manufacturer offers quantity discounts per the following discount schedule:

Option Plan Quantity Price
A 1 - 2,399 $4.00
B 2,400 - 4799 $3.95
C 4,800+ $3.75

A large big-box retailer expects to sell 4,800 units this year. This retailer estimates that it incurs an internal administrative cost of $180 each time it places an order with the manufacturer. Holding cost for the retailer is $50 per case per year. (There are 48 units or water bottles per case.)
Based on this information, and not taking into account any quantity discount offers, what is the calculated EOQ (in units)?

Answer 1

The calculated Economic Order Quantity (EOQ) for the water bottles, without considering quantity discounts, is 1,288 units when rounded to the nearest whole unit.

Step-by-step explanation:

To calculate the Economic Order Quantity (EOQ) for the outdoor equipment manufacturer's water bottles, we can use the EOQ formula, which is given by:

EOQ = √((2DS) / H)

where:

• D is the demand in units (the retailer expects to sell 4,800 units)
• S is the ordering cost per order ($180)
• H is the holding cost per unit per year

To find the holding cost per unit per year, we first calculate the holding cost per case by dividing the total holding cost by the number of cases:

Holding cost per case = $50

Since there are 48 bottles in each case, we calculate the holding cost per unit as follows:

Holding cost per unit (H) = $50 / 48 = $1.041667 per unit per year

Now, we can calculate the EOQ:

EOQ = √((2 * 4,800 * 180) / 1.041667)

EOQ = √(1,728,000 / 1.041667)

EOQ = √(1,658,914.6)

EOQ = 1287.81 units

Since the EOQ must be a whole number, we can round up to the nearest whole unit resulting in an EOQ of 1,288 units.