Chapter 3: Q. 26 (page 288)

Use optimization techniques to answer the questions in Exercises 25–30.
Find two real numbers x and y whose sum is $36$ and whose product is as small as possible.

Short Answer

Expert verified

The two real numbers are $x = 18$ and $y = 18$ .

Step by step solution

Step 1. Given Information.

The sum of two real numbers is $36$ and the product is as small as possible.

Step 2. Form an equation.

From the given information,

$x + y = 36 y = 36 - x f (x) = x y = x (36 - x)$

Step 3. Find the critical points.

$f (x) = x (36 - x) f' (x) = \{\begin{cases} 36 x + 2 x, x < 0 \\ 36 x - 2 x, x \geq 0 \end{cases} f' (x) = 0 36 - 2 x = 0 2 x = 36 x = 18$

Step 4. Find y.

Substitute the value of x in the equation,

$y = 36 - x = 36 - 18 = 18$

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Use optimization techniques to answer the questions in Exercises 25–30.
Find two real numbers x and y whose sum is $36$ and whose product is as small as possible.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Form an equation.

Step 3. Find the critical points.

Step 4. Find y.

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Use optimization techniques to answer the questions in Exercises 25–30.Find two real numbers x and y whose sum is 36and whose product is as small as possible.

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Form an equation.

Step 3. Find the critical points.

Step 4. Find y.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Applied Mathematics

Probability and Statistics

Mechanics Maths

Geometry

Study anywhere. Anytime. Across all devices.

Use optimization techniques to answer the questions in Exercises 25–30.
Find two real numbers x and y whose sum is $36$ and whose product is as small as possible.