This extreme value problem has a solution with both a maximum value and a minimum value. Use Lagrange multipliers to find the extreme values of the function subject to the given constraint.
f(x, y, z) = 6x + 6y + 5z; 3x2 + 3y2 + 5z2 = 29
Max value ________
Min value ____________

Answers

Answer 1

The max value and min value can then be determined from these critical points.

To find the extreme values of a function subject to a constraint, we can use Lagrange multipliers. First, we set up the Lagrangian equation by multiplying the constraint by a scalar λ and adding it to the original function.

Then, we take the partial derivatives of the Lagrangian equation with respect to each variable and set them equal to zero. This will give us a system of equations to solve for the critical points.

Once we have the critical points, we need to determine which ones are maximums and which are minimums.

To do this, we can use the second derivative test. If the second derivative is positive at a critical point, it is a minimum. If the second derivative is negative, it is a maximum.

In summary, to find the extreme values of a function subject to a constraint using Lagrange multipliers, we set up the Lagrangian equation, solve for the critical points, and then use the second derivative test to determine which ones are maximums and which are minimums.

To learn more about : max value

https://brainly.com/question/30236354

#SPJ11

Answer 2

The maximum value of f(x, y, z) is 26.5, and the minimum value is -29.

How did we get the values?

To find the extreme values of the function f(x, y, z) = 6x + 6y + 5z subject to the constraint 3x² + 3y² + 5z² = 29 using Lagrange multipliers, set up the following system of equations:

1. ∇ f = λ∇g

2. g(x, y, z) = 3x² + 3y² + 5z² - 29

where ∇f and ∇g are the gradients of f and g respectively, and λ is the Lagrange multiplier.

Taking the partial derivatives, we have:

∇ f = (6, 6, 5)

∇g = (6x, 6y, 10z)

Setting these two gradients equal to each other, we get:

6 = 6λx

6 = 6λy

5 = 10λz

Dividing the first two equations by 6\(\lambda\), we obtain:

x = ¹/λ

y = ¹/λ

Substituting these values into the third equation, we have:

5 = 10λz

z = ¹/2λ

Now, substitute x, y, and z back into the constraint equation to find the value of λ:

3(¹/λ)² + 3(¹/λ)² + 5(1/2λ)² = 29

6(¹/λ²) + 5(⁴/λ²) = 29

24 + 5 = 116λ²

116λ² = 29

λ² = ²⁹/₁₁₆

λ = ±√²⁹/₁₁₆

λ = ± √²⁹/2√29

λ = ± ¹/₂

We have two possible values for λ, λ = ¹/₂ and λ = ¹/₂

Case 1: λ = ¹/₂

Using this value of λ, we can find the corresponding values of x, y, and z:

x = ¹/λ = 2

y =¹/λ = 2

z = 1/2 λ = ¹/₂

Case 2: λ = -1/2

Using this value of λ, find the corresponding values of x, y, and z:

x = 1/λ = -2

y = 1/λ = -2

z = 1/(2λ) = -1

Now that we have the values of x, y, and z for both cases, substitute them into the objective function f(x, y, z) to find the extreme values.

For Case 1:

f(x, y, z) = 6x + 6y + 5z

= 6(2) + 6(2) + 5(1/2)

= 12 + 12 + 2.5

= 26.5

For Case 2:

f(x, y, z) = 6x + 6y + 5z

= 6(-2) + 6(-2) + 5(-1)

= -12 - 12 - 5

= -29

Therefore, the maximum value of f(x, y, z) is 26.5, and the minimum value is -29.

learn more about Lagrange multipliers: https://brainly.com/question/4609414

#SPJ4


Related Questions

Estelle's graduation picnic will cost $15 if it has 5 attendees. If there are 26 attendees, how much will Estelle's graduation picnic cost? Solve using unit rates.

Answers

Answer:

You can try to do a direct rule of three in this exercise.

We can considerr that the relation is proportional and we know that in this case it's dorect, as the more attendees there come, the more Estelle will have to pay, so we can write this and get x:

5 attendees - 15 dollars

26 attendees -  x dollars

x = 26*15 /  5 = 78 dollars

So you know how much Estelle would have to pay

Write a ratio for the following situation. For every 10 toes, there are 2 feet.

Answers

Answer:

5:1

Step-by-step explanation:

10 toes = 2 feet

10:2

Simplify!

5:1

En un almacén de dimensiones 5m de largo ,3m de ancho y 2m de alto queremos almacenar cajas de dimensiones 10 dm de largo 6dm de ancho y 4 dm de alto ¿cuántas cajas podremos almacenar?

Answers

Answer:

how do you translate

Step-by-step explanation:

given teach trig ratio as a fraction in simplest form:sin(N)

Answers

Answer:

Choice #1: sq rt 3/2

Step-by-step explanation:

cos N=8/PN

PN=16

tan N=PO/8

PO=13.86

sin N=13.86/16=0.866=sq rt 3/2

O is the center of a circle if angle AOB =55° what is angle ACB=?​

Answers

Answer:

answer is 55/2 which is 27.5 degree

Step-by-step explanation:

angle subtended at center is double the angle subtended on aby other part of the circle...

Someone plz help me with this question with an explanation

Answers

To use the angle-angle similarity theorem you need to know 2 corresponding angles of each triangle are the same.

You are already shown that angles H and M are the same.

The sets of corresponding angles are:

H and M, N and I, and O and J

The answer would be angle O and angle J are similar.

Please help!!

What is the value of Avogado's number?

Answers

Answer:

It will be C because I have it in my notes lol

Step-by-step explanation:

Hope this Helped

27 of the 180 vehicles in a movie theater parking lot are minivans.What percent of the vehicles in the parking lot are minivans?

Answers

Answer:

160

Step-by-step explanation:

Answer:

15 percent

Step-by-step explanation:

First use the equation part over total to get 27/180. Then reduce the equation by dividing both the numerator 27 and the denominator 180 by 9. You are left with 3/20. Then use your calculator or you can work it out long hand to get 0.15. You times 0.15 by 100 if you want to find the percent, leaving you with 15 percent.

I hope this helped! :)

The face of a clock has a circumference of 14π inches. What is its area?

Answers

Answer:

A = 49π

Step-by-step explanation:

C = πd

if d = 14 then r = 7

A = πr²

A = π · 7²

A = 49π

Raj is thinking of a fraction that is equivalent to 5/8 in which the numerator is greater than 20 and the denominator is less than 50. What is the fraction Raj is thinking about?

Answers

Answer:

25/40

Step-by-step explanation:

5 into 8 is 40 and 5 into 5 is 25

Answer:

20 / 32

but the numerator is equal to 20, not greater than 20.

Step-by-step explanation:

5/8 = 10/16 = 20 / 32

The graph of a linear function is often a parabola.
True or False

Answers

False




.......
.........

A linear function has a graph as a straight line so the given statement is False.

What is a linear function?

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values.

A linear function is given by

y = mx + c where m is the slope and constant.

Since it is constant it means it should be a straight line in coordinate geometry.

Therefore a linear function always makes a straight line, not a parabola.

Hence "A linear function has a graph as a straight line so the given statement is False".

For more about the linear function,

brainly.com/question/21107621

#SPJ6

Given the function f(x) graphed on the coordinate plane 15
below, determine f(3).

F(3)= ?

Answers

Answer:

2

Step-by-step explanation:

Use the ordered pairs shown in the table.

Which equation represents the data in the
table?

Answers

Answer:

Option C y = 1.5x

Step-by-step explanation:

If you look closely you will notice that there is a pattern that follows all the time. And the pattern is...

y = 1.5x

Simplify (6ab3c)(-abc2).

6b 2c
-6a 2b 4c 3
-6ab 3c 2

Answers

Answer: The simplified version of (6ab3c)(-abc2) is -12a^2 b^4 c^2

Step-by-step explanation:

Answer:

−6a^2b^4c^3

Step-by-step explanation:

Help me with the area of the following triangle??? 25 POINTS question

Answers

-13/2x+1 is the answer which the area

How to find it simple:

Do 1/2*3x-4

then use that answer and multiple it with the height which is 2x+1 and you get the answer.

3x - 5 = -3 is the answer positive or negative

Answers

Answer:

positive

Step-by-step explanation:

if you time the three by a postive then times that by a negetive you get a negitive if you time by two negitives you get postive

In the expression 3x - 5 = - 3 the value of x is positive 2/3.

What is a numerical expression?

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, An expression 3x - 5 = - 3.

3x = - 3 + 5.

3x = 2.

x = 2/3 so x is positive.

learn more about numerical expressions here :

https://brainly.com/question/29199574

#SPJ2




Hamburgers cost $4.50 at a football stadium, write an equation that shows the total cost,c of n hamburgers?

Answers

Answer:

c=4.50

Step-by-step explanation:

c=4.50 the answer is at the top.

Answer:

N=$4.50

Step-by-step explanation:

If the price for one hamburger is $4.50, then N=$4.50

POR QUE ES IMPORTANTE LA GEOMETRIA EN NUESTRA VIDA

Answers

Step-by-step explanation:

La geometría permite a los estudiantes conectar objetos cartográficos en el aula con contextos del mundo real con respecto a la dirección y el lugar. La comprensión de las relaciones espaciales también se considera importante en el papel de la resolución de problemas y las habilidades de pensamiento de orden superior.

15% of 130 using the decimal method

Answers

Answer:

0.3846 is a decimal and 38.46/100 or 38.46%is the percentage for 50/130

Step-by-step explanation:

Pls mark me in brain list

Answer:

0.3846 is a decimal and 38.46/100 or 38.46%is the percentage for 50/130

Step-by-step explanation:

which number is composite? 11,2,9,5​

Answers

Answer:

Answer is 9.

Step-by-step explanation:

Composite number is 9.

I hope it's helpful!

A composite number is a integer that can be formed by multiplying two smaller integers. 11 would not be one because it can only be multiplied by (11x1) however 9 can be formed by 1x9 and 3x3

What is the length of the diagonal of a 10 cm by 15 cm rectangle

Answers

Answer:

5 root 13

Step-by-step explanation:

using the pytogorean therom we get

root(10 squared +15 squared)

=root(100+225)

=root(325)

=5 root 13

A movie theater is located at (1,7) after walking 6 blocks to the movie theater you meet you friend at your friend's house. What ordered pair corresponds to the location of your friend's house

Answers

Answer:

(-5,1)

Step-by-step explanation:

Given the coordinate of the location of the theatre as (1,7)

If this was the coordinate after moving 6 blocks to your friend's house, then the coordinate of the location of my friend house will be gotten as thus;

C = (1-6, 7-6) (since he moved 6blocks)

C = (-5, 1)

Hence the required coordinate is (-5,1)

In the rhombus,
mZ1 =15x, mZ2 = x+y, and m/3 =9z.
Find the value of each variable. The diagram
is not to scale.
2 | 1
a. x = 12, y = 84, z = 20
b. x = 6, y = 174, z = 20
c. X= 6, y = 84, z = 10
d. x = 12, y = 174, z = 10

Answers

For the M1 angle, we can conclude the size of angle is 90°. Do the angle equation like this :

15x=90

x = 90/15

x = 6

Do the same thing in M2 :

Subtitute the x value to equation, then evaluate the value by using 90 because it's the same.

x+y=90

6+y=90

y=90-6

y=84

M3 value is same, 90°

9z=90

9z/9 = 90/9

z=10

Hope this helps

Helllllllp
Simplify the expression 43 + 2(3 − 2).

14
16
66
68

Answers

Answer:

68

Step-by-step explanation:

Answer:

The answer is 46...i cant find that answer in the choices though

Step-by-step explanation:

In PEMDAS we can see that we have parentheses first so we solve whatever is in the parentheses. which 3-2 = 1....so it should look like this

43 + 2 + 1

Which equals 46

hope this helps. have a good day

8p - p+0.75 = 4 + 0.25

Answers

P=0.5 :) your welcome

What is 30% of 42
I’ve given up on my homework please help

Answers

30% of 42 is 12.6.

sorry if wrong.

hope it helps.

have a great day.

Answer:

30% of 42 is 12.6.

Step-by-step explanation:

Ok, so first you need to find the value of 1%. To do that, you divide 42 by 100. That gives you 0.42. So, 0.42 = 1%. TO find 30%, multiply the value of 1% by 30. That's 0.42 * 30, which gives you 12.6. Therefore, 30% of 42 is 12.6!

Translate X(2,3) Y(0,0) Z(4,4) 2 units right and 3 units up

Answers

Answer:

X(4, 6) Y(2, 3) Z(6, 7)

Step-by-step explanation:

If you want to translate something right on a number line, then you are essentially adding to it. Thus you would just add 2 to each of the x values of the coordinates. The same applies with translating something up, all that really means is that you are adding to each of the y values so all you have to do is add 3 to each of the y values and you get your answer.

Answer:

X:(4,6), Y:(2,3), Z:(6,7)

Step-by-step explanation:

2 units right implies a change on the x-axis, meaning you add 2 units to the x of the coordinate pair (x, y). 3 units up implies a change in Y, you apply the same rule and add 3 to the Y of the pair.

2 units right (add 2 to x pair coordinate)

X: (2,3) --> (4,3)

Y: (0,0) --> (2,0)

Z:(4,4) --> (6,4)

and 3 units up (add 3 to y pair coordinate)

X: (4,3) --> (4,6)

Y: (2,0) --> (2,3)

Z: (6,4) --> (6,7)

brainliest to whoever can answer questions correctly ​

Answers

Answer:

v ~ 32.72

Hope that helps!

how to factorise
25x²- 64y²​

Answers

Answer:

(5x + 8y)(5x - 8y)

Step-by-step explanation:

Since both terms are perfect squares, factor using the difference of squares formula, a^2 - b^2 = (a + b)(a - b) where a = 5x and b = 8y.

~Hoped this helped~

25x²- 64y²

= (5x)² - (8y)²

= (5x-8y)(5x+8y)

Hope this helps!

Distribute Terms
-5(x +2)

Answers

-5x-10

hope that helps^^

Other Questions
In Mr. Johnsons third and fourth period classes, 30% of the students scored a 95% or higher on a quiz. Let be the total number of students in Mr. Johnsons classes. a. If 15 students scored a 95% or higher, write an equation involving that relates the number of students who scored a 95% or higher to the total number of students in Mr. Johnsons third and fourth period classes. b. Solve your equation in part (a) to find how many students are in Mr. Johnsons third and fourth period classes the electron configuration of a chromium atom is a. [ar]4s24d3. b. [ar]4s24p4. c. [ar]4s23d3. d. [ar]4s23d4. e. [ar]4s13d5. what is the linear density of a 4.4 m long string, if its mass is measured to be 1.01 kg? suppose you have 450.0 ml of a 0.250 m sodium hydroxide solution. how many moles of sodium hydroxide are in the solution? If the integral from 1 to 5 f(x)dx=10 and the integral 4 to 5 f(x)dx=3.3, find the integral from 1 to 4 f(x)dx. determine the area of the given region under the curve. y = 1/x6 let the timerclocksource=smclk,timermode=continuous, and timerclockdivider=6, what is the time period (in ms) between taifg flags? does a tariff make consumers or producers better off or both or neither Joe King thinks he is "top notch" and buys a bouquet of flowers to pass out to all the ladies... The bouquet has 7 purple tulips, 9 yellow daisies and 12 pink roses. He grabs a flower from the bouquet and gives it to Anita Bath. Then Joe grabs another flower and gives it to Lois Price.What is the probability that Anita gets a purple tulip and Lois gets a pink rose? solve 8 cos 2 ( t ) 2 sin ( t ) 7 = 0 for all solutions 0 t < 2 Brent decides to purchase ground beef to make tacos rather than pricier steak because his weekly budget restricts his expenditure on food.Brent is acting as a rational consumer in that he is recognizing that __________.he is spending beyond his budget to feed his familyhe needs to stay within his budget constrainthe is purchasing where his marginal cost is greater than his marginal benefithe is keeping his total costs below his variable costs Which point are either in quadrant II or quadrants IV Which statement is correct regarding adolescents today compared to adolescents in the 19th century?Adolescent girls are beginning menstruation earlier.Adolescents are exhibiting signs of sexual maturity and puberty much later.Adolescents are attaining shorter heights in adulthood.Adolescents are exhibiting advanced levels of intellectual and emotional growth much sooner. List different techniques used in computer aided education and give comparative analysis of them in short PLEASE ADVICE HOW TO USE THIS SITE you are given two strings that each have length n. you must find their lcs; not only its length. you are allowed polynomial time to do this but you must only use linear space. describe how to do this. a point moves in a plane such that its position is defined by x = ln2t and y = 3 t^3. find the acceleration vector when t = 2.2305/16325/4[-1/4, -12][-1/2,-12] fasb is concerned with making sure that everyone using financial reports is____ How is a corporation different from a sole proprietorship? refere to act1 scene2 Identify and discuss the theme which is evident in the way Mr m talks about their relationship with Thami in the extract