SECTION 1.6 MATHEMATICAL MODELS: CONSTRUCTING FUNCTIONS MATHEMATICAL MODELS: CONSTRUCTING FUNCTIONS.

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Presentation transcript:

SECTION 1.6 MATHEMATICAL MODELS: CONSTRUCTING FUNCTIONS MATHEMATICAL MODELS: CONSTRUCTING 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 where 0 < p < 25. Express the revenue R as a function of x.

DEMAND EQUATION x = - 20p 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 where 0 < p < 25. x = - 20p R = xp Find the maximum Revenue.

EXAMPLES DO EXAMPLES 3, 5, AND 6 DO EXAMPLES 3, 5, AND 6

CONCLUSION OF SECTION 1.6 CONCLUSION OF SECTION 1.6