Find three positive numbers whose sum is 100 and whose product is a maximum.

Answers

Answer 1

Answer:

The numbers are;

x = 100/3,  y = 100/3,  z = 100/3

Step-by-step explanation:

Given the data in the question;

so let the numbers be; x , y and z

so

x + y + z = 100

now

G(x,y,z) = x + y + z - 100

F(x,y,z) = xyz

Fx = yz, Gx = 1

Fy = xz, Gy = 1

Fz = xy, Gz = 1

Fx = λ × Gx

yz = λ

Similarly, xz = lambda

And xy = lambda

From above clearly, x = y = z

x + y + z = 100

so

3x = 100

x = 100/3

since, x = y = z therefore, each number is equal to 100/3

x = 100/3,  y = 100/3,  z = 100/3

Answer 2

We want to find 3 positive numbers such that their sum is 100 and the product is maximum.

The maximum product is P = 37,025.93

Let's say that our 3 numbers are:

A, B, and C.

We must have:

A + B + C = 100

The product of these 3 numbers is:

P = A*B*C

For the restriction, we can write:

A = 100 - B - C

Now we can replace that in the product equation to get:

P = (100 - B - C)*B*C

P = 100*B*C - C*B^2 - B*C^2

Now we want to maximize this, to do it, we need to find the zeros of the derivate of the function. This is a two-variable function, but the dependence on C is exactly the same as the dependence on B, so we can find the zero of deriving with respect to one of these only.

dP/dB = 100*C - 2*C*B - C^2 = 0

             C*(100 - 2*B - C) = 0

One solution is C = 0, the other is:

C = 100 - 2*B

And from the first restroctopm:

A + B + C = 100

we can get:

C = 100 - A - B

Then:

100 - A - B = 100 - 2*B

Then we get A = B

And if we derive the equation for C instead of B, we will get similar results that will lead to:

A = B = C.

This is what maximizes the product, then we have:

A + B + C = 3*A = 100

A = 100/3 = 33.33

P = (33.33)^3 = 37,025.93

This is the maximum product.

If you want to learn more, you can read:

https://brainly.com/question/11212148


Related Questions

(I'LL GIVE BRAINLIEST AND EXTRA POINTS IF YOU HELP!!!)

Answers

Answer:

24/6048 = 252

Step-by-step explanation:

brainlest plz

and why does she have so many beads

Answer:

she said 24 only goes into 60 once, when in reality it can go in twice

Can someone help? I really don’t understand this at all!

Answers

is this pathogroem therom?

How many pounds of grapes can I buy for $1.00?

Answers

2.09

Here you go! Hope it helps!

There are 19.3 cups of flour in a bag. The chef uses 2.9 cups for making cookies.
Then, he uses 1.2 cups of sugar and 5.1 cups of flour for making banana bread.
How many cups of flour are left?

Answers

Answer:

10.1 cups left

Hope this helps!

Can you pls give brainly if this helps

Please help i will give brainlest!​

Answers

Answer:

6×1+9×1/10+4×1/100+7×1/1000

Step-by-step explanation:

4x^10 + 9x^10 what is the sum or difference

Answers

Answer:

[tex]13x^1^0[/tex]

Step-by-step explanation:

[tex]4x^1^0+9x^1^0[/tex]

Add similar elements:

[tex]4x^1^0+9x^1^0=13x^1^0[/tex]

Which number line shows the solution to the inequality 5x + 3> - 17

Answers

Xbdisksme. Dnsjwowke d me

Can someone help me please?

Answers

Answer:

the first one and the last three

Step-by-step explanation:

that should be it.

A, e,d,f........................

Pregnancy length (in days) is a normally distributed random variable with a mean of 266 days and a standard deviation of 16 days. Calculate the z-score for a pregnancy lasting 286 days. Do not round.

Answers

Answer:

it=552

Step-by-step explanation:

with rounding it = 550

The value of z-score for a pregnancy lasting 286 days will be;

⇒ z - score = 1.25

What is Standard deviation?

Standard deviation is the measure of dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.

Given that;

Mean = 266 days

Standard deviation = 16 days

Now,

We know that;

⇒ z - score = (X - μ) / σ

Substitute all the values, we get

⇒ z - score = (286 - 266) / 16

⇒ z - score = 20/16

⇒ z - score = 1.25

Thus, The value of z - score = 1.25

Learn more about the standard deviation visit:

https://brainly.com/question/475676

#SPJ5

PLEASE NEED HELP URGENTLY!


Raul tried to find the midpoint between 5 & 3i and 12 + 7i. Check his work below.

Sum=(5+(-3))+(12+7)i

=2+19i

so the midpoint is 1+ 19over2 i

What mistake did Raul make?


AHe subtracted the values instead of adding them.


BHe did not add the corresponding parts of the complex numbers.


CHe found the sum instead of the average because he forgot to divide by two.


DHe added the numbers in the wrong order.

Answers

Answer:

B.He did not add the corresponding parts of the complex numbers.

Step-by-step explanation:

A mid point is a point that is of equal distance to two reference points.

Given: Find the midpoint of 5+(-3)i and 12+7i.

These expressions have two parts: the value and complex number parts.

Thus the addition ought to have been;

 (5+(-3i)) + (12+7i) = (5 - 3i) + (12 + 7i)

                            = (5 + 12) + (-3i + 7i)

                            = 17 + 4i

The midpoint can be determined as:

                        [tex]\frac{(17 +4i)}{2}[/tex]

Thus it can be observed that Raul did not add the corresponding parts of the complex numbers.

Answer:

bbbbbbbbb

Step-by-step explanation:

An ice cream factory makes 310 quarts of ice cream in 5 hours. How many quarts can they make per hour?

Answers

62 quarts of ice cream can be made in 1 hour. brainliest?

Ben’s favorite deli says the average serving time is 12 minutes. Ben notices that the wait time at the deli varies at different times of day, before and after noon. His observations when the wait time is as advertised can be represented by the equation 2|x − 2| − 12 = 0. Solve for the times when the serving time is as advertised, relative to noon. Group of answer choices (THERES ALOT OF ANSWERS BE PREPARED) SELECT ALL THE ANSWER CHOICES.


4pm,

8pm,

9am,

3pm,

noon,

11am,

6pm,

9pm,

7am,

1pm,

2pm,

5pm,

10pm,

10am,

8am,

7pm,

6am,

Answers

Answer:

8 pm and 8 am

Step-by-step explanation:

Let us solve the equation

[tex]2|(x-2)|-12=0[/tex]

There is a modulus in the equation this means that one value of the modulus will be positive and the other will be negative

Let us solve for the positive first

[tex]2(x-2)-12=0\\\Rightarrow 2x-4-12=0\\\Rightarrow x=\dfrac{16}{2}\\\Rightarrow x=8[/tex]

Now we add this value with 12 noon

So

[tex]12+8=8\ \text{pm}[/tex]

Let us solve for the negative

[tex]2(-(x-2))-12=0\\\Rightarrow 2(2-x)-12=0\\\Rightarrow 4-2x-12=0\\\Rightarrow x=-\dfrac{8}{2}\\\Rightarrow x=-4[/tex]

So

[tex]12-4=8\ \text{am}[/tex]

The times when the serving time is as advertised is 8 pm and 8 am.

What is the value of the expression below?
-8+19+8
ОО
O 11
O 19
O 35

Answers

Answer:

the answer would be 19.

Step-by-step explanation:

-8+8=0

0+19=19

Answer:

19

Step-by-step explanation:

I need help I am in 3grade and I need help with it so if you can please help​

Answers

Answer:

what do you need help with exactly?

Step-by-step explanation:

Answer:

your supposed to ask a question

Step-by-step explanation:

How many 1 6 cup servings are in 3 4 cups of popcorn? (in simplest fraction form)

Answers

Answer: 8/17

Step-by-step explanation: 16 ÷ 34 = 8/17

Hope this helps ^_^

2x^3 + 10x^2 − 4x^2y − 20xy

Factor the entire expression completely. Show the steps of your work.

Answers

Answer:

2x ( x + 5 ) ( x − 2 y )

Step-by-step explanation:

1) factor out 2x from the equation

2) factor out x from the equation

3) factor out -2y from the equation

4) factor out x + 5 from the equation

2x ( x + 5 ) ( x − 2 y )

The expression 2y + 2.7 is equal to for y = 4. ​

Answers

Answer:

10.7

Step-by-step explanation:

i am not certain but since y is the 4 you will have 2(4) + 2.7 so you get 8+2.7 since you do 2x4 then you add 8 and 2.7 to get 10.7

List all sets that -1/3 belongs to.

Answers

Answer:

dfffffffff

Step-by-step explanation:

xcdsw23456iu76

4.497 < 4.387
Is this true?

Answers

Answer:

Yes

Step-by-step explanation:

3x -5y + 2z = -53
x - 7y - 4z = -37
5x+9y+2x = 57

Answers

Answer:

answer is 57

Step-by-step explanation:

3x-5y sshsbwisiehdducux sh

The time taken by artisans A. B and C to do an
embroidery job is 15 hours, 18 hours, and 15 hours.
respectively. A, B, and C begin working together but
after 3 hours B is put on another job. How long will A
and C take to finish the embroidery job?​

Answers

Answer:

3 hours 15mins

Step-by-step explanation:

in 1 hours time, A will complete 1/15 of the job, B will complete 1/18 and C 1/15.

After 3 hours, A completed 3/15 (aka 1/5) of the job, B 3/18 (aka 1/6) and C being the same as A.

total job done after 3 hrs is 1/5 + 1/6 + 1/5 which is 17/30 of the job

left: 13/30

in 1 hr, A and C will do 2/15 of the job (4/30)

therefore, no. of hours needed: 13/4 hours = 3.25 hours (3 hours 15mins)

The perimeter of a rectangle is 212. The length is 16 more than 5 times the width.

Answers

Answer: Length is 15 and width is 91

Step-by-step explanation:

If the length is 16 more than 5 times the width, that means:

let's say

x=length

y=width

2x+2y=212

If the length is 16 more times than 5 times the width, that means

y=5x+16

now we can substitute all y's for 5x+16:

 2x+(5x+16)2=212

=2x+10x+32=212

=12x+32=212

=12x=180

x=15

If the length is 15, the width is

15*2+2y=212

=30+2y=212

=182/2

y=91

Answer:

width 91 length 15

Step-by-step explanation:

2l+2w=212

l=5w+16

2l+2w=212, l=5w+16

substitute

2(5w+16)+2w=212

12w+32=212

12w=180

w=15

L=5w+16

L=5(15)+16

L=91

complete the point-slope equation of the line through (1,0) and (6,-3)

Answers

Answer: y- (-3)= -3/5 (x-6)

Step-by-step explanation:

Answer this question please and i will give brainliest

Answers

Answer:

false the answer is false

Step-by-step explanation:

Can someone help me please

Answers

Answer:  56 degrees

===================================================

Work Shown:

For any triangle, the three interior angles always add to 180

(4x-12) + (6x-17) + (2x+5) = 180

(4x+6x+2x) + (-12-17+5) = 180

12x - 24 = 180

12x = 180+24 ..... adding 24 to both sides

12x = 204

x = 204/12 ..... dividing both sides by 12

x = 17

We can use this x value to find the three angles

4x-12 = 4*17-12 = 56

6x-17 = 6*17-17 = 85

2x+5 = 2*17+5 = 39

As a check,

56+85+39 = 180

which confirms we have the right x value.

We see that 56 is the middle angle, so this is the second largest angle.

Follow the steps to finish solving the equation -3x+ 18=7x

1. Add 3x to both sides to isolate the variable term

2.Divide both sides by 10

PLEASE HELP WILL GIVE BRAINLYEST AND 20 POINTS

Answers

Answer:

9/5=x

Step-by-step explanation:

-3x+ 18=7x

-3x+3x+ 18=7x +3x

18=10x

18/10=10x/10

9/5=x

Answer:

Step-by-step explanation:

- 3x + 18 = 7x

- 3x + 3x + 18 = 7x + 3x ⇔ 18 = 10x

[tex]\frac{18}{10}[/tex] = [tex]\frac{10x}{10}[/tex] ⇔ 1.8 = x

x = 1.8

The value of 100 pennies is ___% of the value of a dollar

Answers

Answer:

The type of coins =pennies  has = 100 pennies.

servant has a total number of 100 coins

The sum of the percentage and pennies = $100

Let us represent the number of nickels as which is _% = 55.4

The number of pennies as y

Step-by-step explanation:

please please help me!!

Answers

Answer:

slope is 4

Step-by-step explanation:

slope of the line is the diference in y /diference in x between any 2 points that belong to the line

slope=(10-2) / (3-1) = 8/2 =4

What is 40x52 To the 7 power

Answers

41,122,868,101,120 would be the answer?

Answer:

168,439,267,742,187,520,000,000

Step-by-step explanation:

40*52=2080

2080^7=168,439,267,742,187,520,000,000

Sarah has saved 254 pound coins. She puts the pound coins into bags.
There are 20 pound coins in each full bag of coins. Sarah is going to take all her full bags of coins to the bank.
She can only take up to 5 full bags of coins to the bank each day.
Sarah wants to go to the bank on as few days as possible.
On how many days will Sarah need to go to the bank?

Answers

Answer:

Step-by-step explanation:

So for the fewest days it would be 3 days. The reason for that is because she has 254 pound coins. And she can inly take 5 bags to the bank a day, all of those 5 bags have 100 pound coins in them. If she take 2 days and get 200 pound coins to the bank. Then on the third day she would only have to bring three bags. So your answer for the fewest days possible is three days!

Hope it helps

3, duh how hard is it for u to solve it
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