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SECTION 2.6. QUADRATIC MODELS: BUILDING QUADRATIC FUNCTIONS. MAXIMIZING INCOME.

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## SECTION 2.6

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**SECTION 2.6**• QUADRATIC MODELS: BUILDING QUADRATIC FUNCTIONS**MAXIMIZING INCOME**A car rental agency has 24 identical cars. The owner of the agency finds that all the cars can be rented at a price of $10 per day. However, for each $2 increase in rental, one of the cars is not rented. What should be charged to maximize income?**DEMAND EQUATION**In economics, revenue R is defined as the amount of money derived from the sale of a product and is equal to the unit selling price p of the product times the number x of units sold. R = xp**DEMAND EQUATION**In economics, the Law of Demand states that p and x are related: As one increases, the other decreases. Example: Suppose x and p obeyed the demand equation: x = - 20p + 500 where 0 < p < 25. Express the revenue R as a function of x.**DEMAND EQUATION**x = - 20p + 500 where 0 < p < 25. Express the revenue R as a function of x. R = xp so in order to write R as a function of x, we have to know what p is in terms of x and then replace p with that expression in R.**DEMAND EQUATION**x = - 20p + 500 where 0 < p < 25. x - 500 = - 20p R = xp Find the maximum Revenue.**EXAMPLES**• Beth has 3000 feet of fencing available to enclose a rectangular field. • a. Express the area of the rectangle as a function of x, the length of the rectangle. • b. For what value of x is the area largest? • c. What is the maximum area?**EXAMPLES**• A farmer with 2000 meters of fencing wants to enclose a rectangular plot that borders on a straight highway. If the farmer does not fence the side along the highway, what is the largest area that can be enclosed?

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