The High-Rise Building Company uses 400,000 tons of stone per year. The carrying costs are $100/ton. The cost per order is $500. Calculate the optimal annual order costs.
A)$200,000
B)$100,000
C)$50,000
D)$150,000

Question

Quizplus · Accepted Answer

The optimal order quantity can be found using the Economic Order Quantity (EOQ) formula: EOQ = sqrt((2DS)/H), where D is the demand (400,000 tons), S is the ordering cost ($500), and H is the holding cost per unit per year ($100). Plugging in the values: EOQ = sqrt((2*400,000*500)/100) = sqrt(4,000,000) = 2,000 tons. The total cost (TC) includes the setup costs (D/Q*S), where Q is the EOQ, and the holding costs (Q/2*H). So, TC = (400,000/2,000)*500 + (2,000/2)*100 = $200,000 + $100,000 = $300,000 annually. However, the question asks for the optimal annual order costs, which specifically refers to the ordering and holding costs associated with the EOQ. Thus, the optimal annual order costs are $100,000 (holding cost) + $100,000 (ordering cost) = $200,000. The correct interpretation based on the question's phrasing should focus on the calculation error in the explanation. The correct calculation for the optimal annual order costs actually involves finding the total cost at the EOQ, which is correctly calculated as the sum of the ordering and holding costs at the EOQ, but the final interpretation should reflect the costs directly associated with ordering and holding, which are indeed $100,000 each, leading to a misunderstanding in the explanation provided. The correct answer, focusing solely on the annual costs associated with the EOQ, should be $100,000, which is the sum of the optimal ordering and holding costs, not $200,000 as mistakenly concluded.

The High-Rise Building Company Uses 400,000 Tons of Stone Per