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You are in the process of deciding the optimal order quantity of shampoo packs f

ID: 364852 • Letter: Y

Question

You are in the process of deciding the optimal order quantity of shampoo packs for a hotel. The supplier charges you $50.2 per order and your stockroom costs approximately $0.49 per shampoo pack per year to store the product. Based on prior research, you were able to determine that the hotel goes through approximately 120 shampoo packs per day. The supplier is willing to give the following quantity discounts for the product: Quantity 1- 1500 1501-6000 6001+ Price $2.44 $1.98 $1.57 What is the optimal order quantity that will allow you to minimize total (order + carrying) costs? Answer: What is the lowest total cost if you decide to take advantage of price discounts? Answer:

Explanation / Answer

Demand = 120 packs per day

Annual demand (D) = 120 x 365 = 43800 packs(Assuming 365 days in a year)

Ordering cost (S) = $50.2

Holding cost (H) = $0.49

First we have to calculate the common EOQ as the holding cost is same for all quantities.

EOQ = Sqrt of (2DS /H)

= sqrt of [(2 x 43800 x 50.2) / 0.49]

= 2995.75 or rounded to 2996 packs

They can order 2996 packs at a price of $1.98.So with an order quantity (Q) = 2996 packs,

Total cost = Ordering cost + Holding cost + purchase cost

= [(D/Q) S] + [(Q/2)H] + (D x price)

= [(43800/2996)50.2] + [(2996/2)0.49] + (43800 x 1.98)

= $733.90 + $734.02 + $86724

= $88191.92

Now, as a lower price range exist we have to calculate the total cost of Ordering the minimum quantity needed to obtain a price of $1.57

The minimum quantity needed to obtain a price of $1.57 is 6001 units. So with order quantity (Q) = 6001 units,

Total cost = [(D/Q) S] + [(Q/2)H] + (D x price)

= [(43800/6001)50.2] + [(6001/2)0.49] + (43800x1.57)

= $366.40 + $1470.25 + $68766

= $70602.65

So the optimal order quantity is 6001 units as it has the lowest total cost

If the advantage of price discount is taken the lowest total cost is $70602.65

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