Question

A pipe manufacturer requires a chemical for making plastic at the rate of 6,000 gallons per year. The cost of keeping the chemical storage includes both the cost of the special security precautions in the storage space and borrowing money on short-term loans to pay for the purchase; this works out to about $10 per gallon per year. Ordering costs, which include cost of special transportation, work out to $200 per order. The chemical is bought at $45 per gallon. What is the EOQ and annual total cost?

Answer 1

The EOQ for the pipe manufacturer is approximately 490 gallons, which minimizes inventory costs. The annual total cost is approximately $272,449. Economies of scale in chemical production, including pipe manufacturing, relate to the disproportionate increase in total costs with an increase in production volume.

Step-by-step explanation:

The Economic Order Quantity (EOQ) is a formula used to determine the optimal order quantity that minimizes total inventory costs. The formula is given by EOQ = √((2DS)/H), where D is the annual demand, S is the ordering cost per order, and H is the holding cost per unit per year.

For the pipe manufacturer's scenario, we have:

• D (Annual demand) = 6,000 gallons
• S (Ordering cost) = $200 per order
• H (Holding cost) = $10 per gallon per year

The EOQ calculation would be:
EOQ = √((2 * 6,000 * 200) / 10) = √(2,400,000 / 10) = √240,000 = 490 gallons (approximately).

The annual total cost (TC) includes the cost of ordering, holding, and purchasing the product. It can be calculated using TC = (D/EOQ) * S + (EOQ/2) * H + DP, where P is the purchase cost per unit. So, the annual total cost would be:
TC = (6,000/490) * 200 + (490/2) * 10 + 6,000 * 45 = √$272,449 (approximately).

Economies of scale in chemical production, such as the case with pipe manufacturing, indicate that increases in production can lead to disproportionate increases in total cost, typically represented by the "six-tenths rule."