The demand for coconut water at SLC WalMart is 600 gallons per week. The setup cost for placing an order to replenish inventory is $25. SLC WalMart incurs an annual holding cost of $2.6/gallon, since coconut water loses its freshness when stored. Assume that there are 52 weeks a year.

Determine SLC WalMart’s Economic Order Quantity in [gallons], to the nearest gallon.

Question

The demand for coconut water at SLC WalMart is 600 gallons per week. The setup cost for placing an order to replenish inventory is $25. SLC WalMart incurs an annual holding cost of $2.6/gallon, since coconut water loses its freshness when stored. Assume that there are 52 weeks a year.

Determine SLC WalMart’s Economic Order Quantity in [gallons], to the nearest gallon.

BlackTom AI · Accepted Answer

The problem presents a classic Economic Order Quantity (EOQ) scenario. First, determine the annual demand: 600 gallons per week for 52 weeks yields D = 600 × 52 = 31,200 gallons per year.
Next, identify the cost parameters: setup (ordering) cost S = $25 per order and annual holding cost per unit H = $2.60 per gallon.
The EOQ formula is EOQ = sqrt(2DS / H). Substituting the known values gives EOQ = sqrt(2 × 31,200 × 25 ÷ 2.60).
Compute the numerator: 2 × 31,200 × 25 = 1,560,000.
Divide by the holding cost: 1,560,000 ÷ 2.60 = 600,000.
Now take the square root: sqrt(600,000) ≈ 774.596..., which is the theoretical EOQ before rounding.
When rounding to the nearest gallon, this value corresponds to about 775 gallons per order.
Thus, using the EOQ framework with the given demand and costs leads to an optimal order quantity on the order of several hundred gallons per replenishment, specifically around 774.6, which rounds to 775 gallons.

OSC 3050-016 Spring 2025 Module 3 Homework

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