HH_15_2 - Lecture notes to accompany Section 15.2 of...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
(11/25/08) Math 10C. Lecture Examples. Section 15.2. Optimization Example 1 The function g ( x , y ) = 2x 2 + y 2 - 2xy - 2y has a global minimum. Find it. Answer: The global minimum is - 2. Example 2 Find, without using calculus, the global maximum of f ( x , y , z ) = 1 ( x - y ) 2 + 1 + e - z 2 and where it occurs. Answer: The global maximum is 2 at the points ( x, x, 0) for all x . Example 3 The function M ( x , y ) = - 5y x 2 + y 2 + 1 , whose graph is shown in Figure 1, has a global maximum and a global minimum. What are they and where do they occur? FIGURE 1 Answer: The global maximum is 5 2 at (0 , - 1) and the global minimum is - 5 2 at (0 , 1). Example 3 Suppose that rectangular boxes with no tops (Figure 2) are to be manufac- tured so that each has a volume of 6 cubic feet. The boxes are to be made from material that costs 6 dollars per square foot for the bottoms, 2 dollars per square foot for the fronts and backs, and 1 dollar per square foot for the sides. What dimensions would minimize the cost of manufacturing each box? FIGURE 2 Answer: The boxes should be manufactured to be 1 foot wide, 2 feet long, and 3 feet high.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Lecture notes to accompany Section 15.2 of Calculus by Hughes-Hallett et al. 1 Math 10C. Lecture Examples. (11/25/08) Section 15.2, p. 2 Example 5 The function N ( x , y ) = 1 x + 1 y + xy has a minimum for x > , y > . What is it and where does it occur? Answer: The minimum is 3 at (1 , 1). Example 6 What are the values of x and y such that the sum of the squares of the distances from the point ( x , y ) to the four points ( a 1 , b 1 ) , ( a 2 , b 2 ) , ( a 3 , b 3 ) , and ( a 4 , b 4 ) is a minimum? Answer: x = 1 4 ( a 1 + a 2 + a 3 + a 4 ) y = 1 4 ( b 1 + b 2 + b 3 + b 4 ) (The averages) Interactive Examples Work the following Interactive Examples on Shenks web page, http//www.math.ucsd.edu/ashenk/: Section 15.1: Examples 16 The chapter and section numbers on Shenks web site refer to his calculus manuscript and not to the chapters and sections of the textbook for the course....
View Full Document

This note was uploaded on 09/30/2011 for the course MATH 10C taught by Professor Hohnhold during the Spring '07 term at UCSD.

Page1 / 2

HH_15_2 - Lecture notes to accompany Section 15.2 of...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online