QUADRATIC MODELS: BUILDING QUADRATIC FUNCTIONS

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SECTION 2.6

• QUADRATIC MODELS BUILDING QUADRATIC FUNCTIONS

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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?
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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
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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 25. Express the revenue R as a function of x.
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DEMAND EQUATION
x - 20p 500 where 0 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.
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DEMAND EQUATION
x - 20p 500 where 0 - 20p
R xp
Find the maximum Revenue.
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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?

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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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• CONCLUSION OF SECTION 2.6