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Homework Homework Assignment #27 Review Section 4.6 Page 265, Exercises: 1 – 29 (EOO),19, skip 17 Quiz next time Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

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Homework, Page 265 1.Find the dimensions of the rectangle of maximum area that can be formed from a 50-in. piece of wire. (a) What is the constraint equation relating the lengths x and y of the two sides? 2x + 2y = 50 (b) Find a formula for the area in terms of x alone. (c)Does the problem require optimization over an open interval or a closed interval? The problem requires optimization on a closed area. (d)Solve the optimization problem. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

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Homework, Page 265 1. (d)Solve the optimization problem. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

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Homework, Page 265 5.Find the positive numbers x and y such that xy = 16 and x + y is as small as possible. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

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Homework, Page 265 9.Suppose 600 ft. of fencing are used to enclose a corral in the shape of a rectangle with a semicircle whose diameter is a side of the rectangle. Find the dimensions of the corral with maximum area. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

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Homework, Page 265 9.Continued. Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

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Homework, Page 265 13.Find the point P on the parabola y = x 2 closest to the point (3, 0). Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

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Homework, Page 265 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

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Homework, Page 265 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company 19.Continued.

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Homework, Page 265 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company 21. What are the dimensions of the cylinder of the largest volume that can be inscribed in the sphere of radius R?

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Homework, Page 265 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company 21. Continued.

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Homework, Page 265 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company 25.Consider a rectangular warehouse consisting of n separate spaces of equal size. Assume that wall materials cost $200 per linear ft and the company allocates $2,400,000 for the project. Find a formula in terms of n for the maximum possible area of the warehouse.

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Homework, Page 265 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company 29.Find the maximum area of a triangle in the first quadrant formed by the x-axis, the y-axis, and the tangent to y = (x + 1) –2

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Example, Page 265 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company 32.An 8-billion bushel corn crop brings a price of $2.40/bushel. A commodity broker uses the rule of thumb: If the crop of reduced by x percent, then the price increases by 10x cents. Which crop size results in the maximum revenue and what is the price per bushel?

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Example, Page 265 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company 36.Figure 21 shows a rectangular plot of size 100 X 200 ft. Pipe is to be laid between points A and C by way of point P. The cost of laying pipe through the lot is $30/ft ant the cost along the side is $15/ft. (a) Let f (x) be the total cost, where x is the distance from P to B. Determine f (x), noting f is discontinuous at x = 0.

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Example, Page 265 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company 36.(b) What is the most economical way to lay the pipe? What if the cost along the side is $24/ft?

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Homework Homework Assignment #28 Read Section 4.7 Page 265, Exercises: 31, 39, 43, 47, 53, 59 Rogawski Calculus Copyright © 2008 W. H. Freeman and Company

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