6. Graphical Applications of Derivatives

Applied Optimization

6. Graphical Applications of Derivatives

Applied Optimization

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Multiple Choice

A small clinic uses 5,000 bottles of hand sanitizer per year. Each shipment costs $200 to order, and it costs $1 to store each bottle for a year. How many bottles should the clinic order in each shipment to minimize the total ordering and storage costs?

1414 bottles

2512 bottles

1008 bottles

943 bottles

Verified step by step guidance

Step 1: Recognize that this is an Economic Order Quantity (EOQ) problem. The EOQ formula minimizes the total cost of ordering and storing inventory. The formula is given by:

Q = \sqrt{\frac{2 D S}{H}}

, where Q is the optimal order quantity, D is the annual demand, S is the ordering cost per order, and H is the holding cost per unit per year.

Step 2: Identify the given values from the problem. The annual demand (D) is 5,000 bottles, the ordering cost per order (S) is $200, and the holding cost per unit per year (H) is $1.

Step 3: Substitute the given values into the EOQ formula. This gives:

Q = \sqrt{\frac{2 \times 5000 \times 200}{1}}

Step 4: Simplify the expression under the square root. First, calculate the numerator:

2 \times 5000 \times 200

. Then divide the result by the denominator, which is 1.

Step 5: Take the square root of the simplified value to find the optimal order quantity (Q). This will give the number of bottles the clinic should order in each shipment to minimize total costs.

1:13m

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