Question

Demand for an item is 21584 units per year. Each order placed costs $83. The annual carrying cost percentage per item in inventory is 18% each. The variable purchase cost is $2.50 per unit if less than 3000 units will be ordered, $2.40 from 3000 units upto (but not including 4000 units), and $2.30 for at least 4000 units. These are all-units discounts.

What is the optimal order quantity Q for the unit cost of $2.30? ____

Answer 1

The optimal order quantity (Q) for the unit cost of $2.30, calculated using the Economic Order Quantity (EOQ) formula, is 2942 units.

Step-by-step explanation:

To determine the optimal order quantity (Q) for the unit cost of $2.30, we can use the Economic Order Quantity (EOQ) model, which minimizes the total inventory costs, which include both ordering costs and carrying costs.

The formula for EOQ is given by:

EOQ = √((2DS)/H)

Where:

• D is the annual demand (21584 units)
• S is the order cost ($83 per order)
• H is the annual holding cost per unit

Since H is given as a percentage (18%), we first calculate H using the unit cost for which we want the EOQ:

H = C * i

Where:

• C is the unit cost ($2.30)
• i is the carrying cost percentage (18% or 0.18)

Substituting the values, we get H = $2.30 * 0.18 = $0.414 per unit per year.

Now we can calculate the EOQ:

EOQ = √((2 * 21584 * 83) / 0.414)
EOQ = √(3582928 / 0.414)
EOQ = √(8653387.681)
EOQ = 2941.69

Since EOQ must be an integer, we round to the nearest whole number. The EOQ for the unit cost of $2.30 is 2942 units.