   Chapter 7.5, Problem 35E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Finding Positive Numbers In Exercises 33-36, fine three positive numbers x, y, and z that satisfy the giver conditions.The sum is 60 and the sum of the squares is a minimum.

To determine

To calculate: The three positive numbers x, y and z if their sum is 60 and the sum of the squares is a minimum.

Explanation

Given Information:

The sum of three numbers x, y and z is 60 and the sum of the squares is a minimum.

Formula used:

If the function y=f(x) has a maximum at a point then their first partial derivatives fx(x) and fy(x) at that point are zero.

Calculation:

Consider the three numbers be x, y and z.

The sum of three numbers x, y and z is 60.

x+y+z=60z=60xy

The sum S of the squares is a minimum.

S=x2+y2+z2

Substitute z=60xy in the equation S=x2+y2+z2,

S=x2+y2+(60xy)2

Now, the first partial derivatives are,

Sx=2x+2(60xy)(1)=2x120+2x+2y=4x+2y120=2(2x+y60)

And

Sy=2y+2(60xy)(1)=2y120+2x+2

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