Vilas County Hospital consumed 400 boxes of bandages per week last year. The price of bandages was $80 per box, and the hospital operates 52 weeks per year. The cost of processing an order was $64, and the cost of holding one box throughout a full year was 20% of the value of the material. Last year the hospital ordered bandages, on average, once every two weeks, each time ordering 800 boxes. What extra cost did the hospital incur that could have been avoided if the EOQ concept had been applied?

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BlackTom AI · Accepted Answer

We begin by parsing the problem to extract all the given data and the quantity of interest. The hospital’s annual demand D is 400 boxes/week × 52 weeks = 20,800 boxes. The current ordering policy is every two weeks, so the order quantity Q_current is 800 boxes and the number of orders per year is D/Q_current = 20,800 / 800 = 26 orders. The annual ordering cost under current policy is S × (D/Q) = 64 × 26 = 1,664 dollars. The annual holding cost uses the average inventory level, which under current policy is Q/2 = 800/2 = 400 boxes. The annual holding cost per box is 20% × $80 = $16, so total holding cost is 400 × 16 = 6,400 dollars. Therefore the total annual inventory cost under the current policy is 1,664 + 6,400 = 8,064 dollars.

Now we compute the EOQ (Economic Order Quantity). The EOQ formula is EOQ = sqrt(2DS/H), where D = 20,800, S = $64 per order, and H is the annual holding cost per unit, which is 20% of the unit cost: H = 0.20 × $80 = $16. Substituting, EOQ = sqrt(2 × 20,800 × 64 / 16) = sqrt((41,600 × 64) / 16) = sqrt(2,662,400 / 16) = sqrt(166,400) ≈ 408 boxes.

With EOQ, the number of orders per year is D/EOQ ≈ 20,800 / 408 ≈ 51 orders. The annual ordering cost under EOQ is S × (D/EOQ) ≈ 64 × 51 ≈ 3,264 dollars. The average inventory under EOQ is EOQ/2 ≈ 408/2 ≈ 204 boxes, so the annual holding cost is H × (EOQ/2) ≈ 16 × 204 ≈ 3,264 dollars. Therefore the total annual inventory cost under EOQ is approximately 3,264 + 3,264 = 6,528 dollars.

Finally, we compare the current total (about $8,064) with the EOQ total (about $6,528). The potential annual savings from adopting EOQ would be 8,064 − 6,528 ≈ 1,536 dollars. This figure is greater than 1,450 dollars, so the amount of extra cost that could have been avoided falls into the range indicated by choices describing costs above 1,450 dollars. The remaining options either cap the amount too low or place it in nearby ranges that do not cover 1,536.

MGS310001.2025FA Test 03: Chap 10,11

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MGS*3100*01.2025FA Test 03: Chap 10,11