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Unformatted text preview: Math Learning Center Boise State ©2010 Quadratic Modeling Business 10 Profits In this activity, we are going to look at modeling business profits. We will allow q to represent the number of items manufactured and assume that all items that are manufactured are also sold. To simplify matters, rather than discussing generic items being manufactured let’s assume we are manufacturing graphing calculators. Sometime later we will need to know what the capacity of our ability to manufacture calculators is: In this case we will say that we have the ability to build at most 15,000 calculators. We are interested in finding the profits as a function of the quantity manufactured, so we will label profits as gG¡¢ . Two other terms that are important in profit are cost and revenue: • Cost is the amount of money spent to manufacture q items. Thus, we will denote cost as £G¡¢u • Revenue is the amount of money earned by selling q items. Thus, we will denote cost as ¤G¡¢u The importance of the cost and revenue functions is that they can be used to compute the profits function which is what we are interested in. The profit function can be found by computing: gG¡¢ ¥ ¤G¡¢ ¦ £G¡¢ Thus, to find the profit function, it will be easier to find both the revenue function and the cost function. Finding the cost function: In a simple model the cost function is based on two parts: • Fixed costs: The costs that will be spent whether or not a single item is built such as mortgage payments on the building, property taxes, and electricity. In this example, let’ say that the fixed costs are $20,000.00....
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 Fall '09
 ALINASCHIMPF
 Math, Algebra, Optimization, Quadratic equation, Math Learning Center

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