2.7 hmwk key 2010
November 12, 2010
2.7 Mathematical Models
page 135 (5, 8, 9, 17)
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2.7 hmwk key 2010
November 12, 2010
5. The price p, in dollars, and the quantity x sold of a certain product obey the demand equation.
x = ­5p + 100
0 < x < 300
a) Express the revenue R as a function of x.
b) What is the revenue if 15 units are sold?
c) Graph.
d) What quantity of x maximizes revenue? What is the maximum revenue?
e) What price should the company charge to maximize revenue?
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2.7 hmwk key 2010
November 12, 2010
8. Enclosing a Rectangular Field along a River: Beth has 3000 feet of fencing available to enclose a rectangular field. One side of the field lies along a river, so only three sides require fencing.
a) Express the area A of the rectangle as a function of x, where x is the length of the side parallel to the river.
b) Graph. For what value of x is the area the largest?
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2.7 hmwk key 2010
November 12, 2010
9. Let P = (x, y) be a point on the graph of y = x2 ­ 8.
a) Express the distance d from P to the origin as a function of x.
b) What is d if x = 0?
c) What is d if x = 1?
d) Graph d = d(x).
e) For what values of x is d smallest?
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2.7 hmwk key 2010
November 12, 2010
17. A rectangle is inscribed in a circle of radius 2. Let P = (x, y) be the point in quadrant I hat is a vertex of the rectangle and is on the circle.
a) Express the area A of the rectangle as a function of x.
b) Express the perimeter p of the rectangle as a function of x.
c) Graph A = A(x). For what value of x is A largest?
d) Graph p = p(x). For what value of x is p largest?
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