# The table whose sum is 19 and product is Maximum.

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

### Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

#### Solutions

Chapter 2, Problem 19P

a.

To determine

## To write: The table whose sum is 19 and product is Maximum.

Expert Solution

So according to the table only possible pairs whose sum is 19 and product is large (9,10)(10,9)

### Explanation of Solution

Given information:

Table of number whose sum is 19 and product is Maximum.

Concept Used:

Let first number is x and second number is y. for maximum product x and y should be positive.

Calculation:

 X(first number) Y(second) Product 1 18 18 2 17 34 3 16 48 4 15 60 5 14 70 6 13 78 7 12 84 8 11 88 9 10 90 10 9 90

Conclusion:

The above values are the two numbers with product as large as possible.

b.

To determine

Expert Solution

### Explanation of Solution

Given information:

First number is x

Second number is y

Sum is 19

Product is Maximum

Concept used:

x+y=19

xy= Product................... 1

x+y=19

x=(19y)..................2

Put equation 2 in equation 1

Product =y(19y)

Product =19yy2

Conclusion:

The required function showing the product is 19yy2

c.

To determine

Expert Solution

### Explanation of Solution

Given information:

Two number whose sum is 19

x+y=19xy= maximize

Concept used:

Maximize the product by using Differentiation

First differentiation is equal to 0 for maximize

Calculation:

Product =y(19y)

p(y)=19yy2

Differentiate with respect to y

p'(y)=192y

Put p'(y)=0 for maximum value

192y=019=2yy=95

Then x=95

Conclusion:

From subpart (a) answer is (9,10) . Here x and y value is 95 . Because in subpart (a) only take the whole number that is why there is difference in the answer.

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