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Business Calculus Applications of Extrema

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Extrema: Applications We will emphasize applications pertaining to business. Basic formulas: Revenue = price * number of items sold Cost = fixed cost + variable cost Profit = Revenue – Cost Salvage Value is the decreased value of an item after time has passed, due to depreciation.

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General Approach to Applications 1.Identify the function to be maximized or minimized. 2.Write the appropriate information and create the formula for this function. 3.Find an appropriate domain for the input variable. 4.Find the critical values and endpoints for the function. 5.Test these values using the appropriate test. 6.Answer the question.

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Hints: Maximize Revenue: If the question is given in terms of changing the price of an item, resulting in a change in the number of items sold, let the variable represent the number of changes in either price or items. Minimize Inventory Cost: Let the variable x represent the lot size for each order through the year. To calculate storage cost, use the average number of items stored: x/2. The number of reorders necessary is found by dividing the total number of items ordered for the year by the lot size for each order. Inventory Cost = Reordering Cost + Storage Cost

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