Final answer:
To find the additional annual cost incurred by the Garden Variety Flower Shop due to not using the EOQ, we need to calculate both the EOQ and the total inventory costs for both the EOQ and the current order size and compare them.
Step-by-step explanation:
To determine the additional annual cost the Garden Variety Flower Shop is incurring by using an order size of 1,500 flower pots instead of an optimal order size, we need to use the Economic Order Quantity (EOQ) model. The EOQ model calculates the most cost-effective quantity to order that minimizes total inventory costs, which include ordering costs and carrying costs. The formula for EOQ is given by:
EOQ = √((2DS)/H), where:
- D is the annual demand (in units).
- S is the ordering cost per order.
- H is the annual holding cost per unit.
In this scenario:
- D = 550 pots per month * 12 months = 6,600 pots per year.
- S = $20 per order.
- H = 30% of the cost per pot = 0.30 * $3.00 = $0.90 per pot per year.
Plugging the values into the EOQ formula, we get:
EOQ = √((2 * 6,600 * 20) / 0.90) ≈ √(146,666.67) ≈ 383 pots.
With the EOQ calculated, we can also determine the total inventory costs for ordering EOQ versus the current order size of 1,500 pots.
Total cost (TC) with EOQ is:
TC = (D/EOQ)S + (EOQ/2)H.
Total cost (TC) with current order size is:
TC = (D/Order Size)S + (Order Size/2)H.
Now, we calculate the additional annual cost incurred by the shop by subtracting the TC with EOQ from the TC with the current order size:
Additional Annual Cost = TC with current order size - TC with EOQ.
Let's calculate these values to determine the additional annual cost of using an order size of 1,500 pots instead of the optimal EOQ.