# Tofind: thetwo positive integers whose sum and product are given below. ### Single Variable Calculus: Concepts...

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

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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