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Average Inventory The Yasuko Okada Fragrance Company (YOFC) receives a shipment of 400 cases of specialty perfume early Monday morning of every week. YOFC sells the perfume to retail outlets in California at a rate of about 80 cases per day during each business day (Monday through Friday). What is the average daily inventory for YOFC? (Hint: Find a function that represents the inventory for any given business day and then integrate.)

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Answer:

Step-by-step explanation:

At the end of any given business day, CFFC has 400-80t cases of perfume on hand, where t = 1 represents Monday, t = 2 represents Tuesday and so on. The inventory becomes nil on Friday evening. So,

The values of a and b are

a = 0

b = 5

Using the formular for average value, we have the average value as

[tex]\frac{1}{5-0}\int\limits^5_0 {(400-80t)}dt\\\\=\frac{1}{5}(400t-\frac{80t^2}{2})\limits^5_0\\\\=\frac{1}{5}(400t-40t^2)\limits^5_0\\\\=\frac{1}{5}(2000-1000)\\\\=200[/tex]

Average inventory is 200 cases

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