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

Homework, Page 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

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

Homework, Page 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

Homework, Page 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

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

Homework, Page 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

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

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

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?

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

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.

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

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?

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.

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?

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