Practical Problems (§ 3.4)
Fall 2011, Math 1210-007
Suggestions for attacking optimization problems:
Step 1: The situation: draw a picture, and assign variables to important quantities.
Step 2: The objective: write a formula for the function Q to be maximized or minimized in terms of your
assigned variables.
Step 3: Last variable standing: identify given conditions of the problem, and eliminate all but one variable;
express Q as a function this remaining variable.
Step 4: Analysis: find all critical points, and determine maximum or minimum value based on previously
learned methods (e.g. comparison, first and second derivative tests).
§3.4 #6
Find the points on the parabola x = 2y 2 that are closest to the point (10, 0).
1 of 4
§3.4 #14
A farmer wishes to fence off three identical adjoining rectangular pens, each with 300 square feet of
area. What should the width and length of each pen be so that the least amount of fence is required?
2 of 4
§3.4 #36
A rectangle is to be inscribed in a semicircle of radius r. What are the dimensions of the rectangle if
its area is to be maximized?
3 of 4
§3.4 #50
An advertising flyer is to contain 50 square inches of printed matter, with 2-inch margins at the top
and bottom and 1-inch margins on each side. What dimensions for the flyer would use the least paper?
§3.4 #37
Of all right circular cylinders with a given surface area a, find the one with the maximum volume. The
ends of the cylinders are closed.
4 of 4