Question

Demand for an item is 21935 units per year. each order placed costs $81. the annual carrying cost percentage per item in inventory is 20% 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. part a: 3 points what is the optimal order quantity q✕ for the unit cost of $2.30? please round to a whole number.

Answer 1

The optimal order quantity (Q*) for a unit cost of $2.30, using the EOQ model and the given parameters, is 279 units when rounded to a whole number.

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) formula. The EOQ model minimizes the total cost of ordering and holding inventory. Given that the demand is 21935 units per year, each order costs $81, and the annual carrying cost per item is 20% of the cost, we can calculate EOQ with the following steps:

• First, determine the carrying cost per unit by multiplying the variable cost per unit ($2.30) by the carrying cost percentage (20%). This yields $0.46 (0.20 * $2.30).
• With the carrying cost per unit, order cost, and annual demand known, EOQ can be calculated using the formula: EOQ = √((2 * Demand * Order Cost) / Carrying Cost per unit).
• Plugging the numbers into the equation, we get EOQ = √((2 * 21935 * 81)/0.46) which simplifies to the square root of 3,656,790 / 0.46, and then approximately 279 units.

Therefore, the optimal order quantity Q* for the unit cost of $2.30, rounded to a whole number, is 279 units.