BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805
BuyFind

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 4, Problem 39RE
To determine

Tofind:thetwo positive integers whose sum and product are given below.

Expert Solution

Answer to Problem 39RE

Two positive integers are 500 and 125 respectively.

Explanation of Solution

Given:

  x+4y=1000 .

  x=1000-4y .

The product of two which can be maximize.

  p=xy .

Concept used:

If d2ydx2>0. the concave will be open upward and local minima can be found.

. d2ydx2<0. the concave will open downward and local maxima can be found.

  y=f(x) is concave upward on those intervals where

  y=f(x)>0 .

  y=f(x) id concave downward on those intervals where

  y=f(x)<0 .

Calculation:

Let x and y be positive integers from the description of the sum and product the equation will be:

  x+4y=1000 .

  x=1000-4y .

The product of two which can be maximize.

  p=xy .

Substituting for x, find p=0

  p=(1000-4y)y=1000y4y2 .

  p=10008y

  0=10008y

  y=125 .

  p=8 .

So p is concave down and y=125 is the maximum.

  x=1000-4y .

  x=500 .

Hence the two positive integers are 500 and 125 respectively.

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