Minimizing a Sum Find two positive numbers whose sum is 100 and the sum of whose squares is a minimum.
To find: The two positive numbers whose sum is 100 and the sum of whose squares is a minimum.
Answer to Problem 20P
The two positive numbers are 50 and 50 whose sum is 100 and the sum of whose squares is a minimum.
Explanation of Solution
Given:
The sum of the numbers is 100 and the sum of whose squares is a minimum.
Formula used:
The minimum of the function occurs at the point,
Calculation:
Let the two numbers be x and y and the sum of whose squares is S.
The sum of the numbers represented as,
Now, get the value of y in terms of x,
The sum of the squares of two numbers is,
Now, compare the sum
And
The minimum function occurs at the point
Substitute
Now substitute 50 for x in the equation (2),
Thus, the two numbers is 50 and 50 whose sum is 100 and the sum of whose squares is a minimum.
Chapter 2 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning