Question

The A\&M Hobby Shop carries a line of radio-controlled model racing cars. Demand for the cars is assumed to be constant at a rate of 50 cars per month. The cars cost $80 each, and ordering costs are approximately $15 per order, regardless of the order size. The annual holding cost rate is 20%.

Determine the economic order quantity and total annual cost (in $) under the assumption that no backorders are permitted. (Round your answers to two deimal places.)
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Answer 1

The economic order quantity (EOQ) is approximately 15.31 cars. The total annual cost is $834.48.

Step-by-step explanation:

To determine the economic order quantity (EOQ), we can use the EOQ formula: EOQ = sqrt((2 * Demand * Ordering Cost) / Holding Cost).

Given:

• Demand = 50 cars per month
• Ordering Cost = $15 per order
• Holding Cost rate = 20%

Plugging in these values into the formula:

EOQ = sqrt((2 * 50 * 15) / (0.2 * 80))

Simplifying the equation:

EOQ = sqrt(3750 / 16)

EOQ = sqrt(234.375)

EOQ ≈ 15.31 (rounded to two decimal places)

Now, to calculate the total annual cost, we need to consider both the ordering cost and the holding cost.

Ordering cost = Number of orders * Cost per order = (Demand / EOQ) * Ordering Cost = (50 / 15.31) * 15 = 49.04 * 15 = $735.60 (rounded to two decimal places)

Holding cost = Average inventory * Holding cost rate * Unit cost = (EOQ / 2) * Holding cost rate * Unit cost = (15.31 / 2) * 0.2 * 80 = 6.18 * 0.2 * 80 = $98.88 (rounded to two decimal places)

Total annual cost = Ordering cost + Holding cost = $735.60 + $98.88 = $834.48