Question

A milk distributor finds that it sells, on average, 100 gallons a weck of organic chocolate milk. For this problem, assume that demand occurs at a constant rate over a 52-week year. Organic chocolate milk is purchased at a price of $4.75 per gallon. The inventory-related holding cost rate is 25%. Each order placed with the supplier costs the distributor $25. What is the order quantity that minimizes the distributor's total inventory-related costs'? 1,020 gallons of organic milk 1,019 gallons of organic milk 65 gallons of organic milk 468 gallons of organic milk

Answer 1

Answer:

468 gallons of organic milk

Explanation:

Economic Order quantity formula

$Q_{opt} = \sqrt{\frac{2DS}{H}}$

Where:

D = annual demand = 100 gallons per week x 52 weeks per year  = 5,200

S= setup cost = ordering cost = $ 25

H= Holding Cost = 25% of the unit cost = 4.75 x 25% = 1.19

$Q_{opt} = \sqrt{\frac{2(5,200)(25)}{1.19}}$

$Q_{opt} = \sqrt{\frac{260,000}{1.19}}$

$Q_{opt} = \sqrt{218947.3684}$

EOQ = 467.9181215