Answer:
x = 250
y = 125
u(x,y) = 3125500
Step-by-step explanation:
As given,
The utility function u(x, y) = 100xy + x + 2y
[tex]P_{x}[/tex] = 2 , [tex]P_{y}[/tex] = 4
Now,
Budget constraint -
[tex]P_{x}[/tex] x + [tex]P_{y}[/tex] y = 1000
⇒2x + 4y = 1000
So,
Let v(x, y) = 2x + 4y - 1000
Now,
By Lagrange Multiplier
Δu = Δv
⇒< 100y + 1, 100x + 2 > = < 2, 4 >
By comparing, e get
100y + 1 = 2 ........(1)
100x + 2 = 4 .........(2)
Divide equation (2) to equation (1) , we get
[tex]\frac{100y + 1}{100x + 2} = \frac{1}{2}[/tex]
⇒2(100y+1) = 1(100x+2)
⇒200y + 2 = 100x + 2
⇒200y = 100x
⇒2y = x
Now,
As 2x + 4y = 1000
⇒2x + 2(2y) = 1000
⇒2x + 2x = 1000
⇒4x = 1000
⇒x = 250
Now,
As 2y = x
⇒2y = 250
⇒y = [tex]\frac{250}{2}[/tex] = 125
∴ we get
x = 250
y = 125
Now,
u(250, 125) = 100(250)(125) + 250 + 2(125)
= 3125000 + 250 + 250
= 3125000 + 500
= 3125500
⇒u(250, 125) = 3125500
The maximized value of the utility function is $3125500
The utility function is given as:
[tex]U(x,y) = 100xy + x + 2y[/tex]
The prices per unit are also given as:
[tex]P_x = 2[/tex]
[tex]P_y = 4[/tex]
When a person receives $1000, then the budget function is:
[tex]2x + 4y = 1000[/tex]
Divide through by 2
[tex]x + 2y = 500[/tex]
Differentiate the utility function with respect to x and y
[tex]U'(x) = 100y + 1[/tex]
[tex]U'(y) = 100x + 2[/tex]
So, we have:
[tex]U'(x) = P_x[/tex] and [tex]U'(y) = P_y[/tex]
The above equations become
[tex]100y + 1 = 2[/tex] and [tex]100x + 2 = 4[/tex]
Divide both equations
[tex]\frac{100y + 1}{100x + 2} = \frac 24[/tex]
Reduce the fractions
[tex]\frac{100y + 1}{100x + 2} = \frac 12[/tex]
Cross multiply
[tex]100x + 2 = 200y + 2[/tex]
Subtract 2 from both sides
[tex]100x = 200y[/tex]
Divide both sides by 100
[tex]x = 2y[/tex]
Recall that:
[tex]x + 2y = 500[/tex]
So, we have:
[tex]2y + 2y = 500[/tex]
[tex]4y=500[/tex]
Divide through by 4
[tex]y=125[/tex]
Recall that:
[tex]x = 2y[/tex]
So, we have:
[tex]x = 2 \times 125[/tex]
[tex]x = 250[/tex]
Also, we have:
[tex]U(x,y) = 100xy + x + 2y[/tex]
Substitute the values of x and y, in the above function
[tex]U(250,125) = 100 \times 250 \times 125 + 250 + 2 \times 125[/tex]
[tex]U(250,125) = 3125500[/tex]
Hence, the maximized value of the utility function is 3125500
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Someone plz help me
Answer:
The answer would be 14 becuase they are adding 6 to every other number.
Step-by-step explanation:
HELP!!! I will Mark Brainiest!!!!
Inga and Aileen are measuring the temperature of frozen hydrogen. Inga is using a thermometer that has increments of 0.25∘F, and she gets a measurement of 3.25∘F. Aileen is using a thermometer that has increments of 0.125∘F, and she gets a measurement of 3.375∘F.
Which thermometer has less uncertainty?
1. Aileen's thermometer, because it has smaller increments.
2. Neither, because the uncertainty in both thermometers is the same.
3. Inga's thermometer, because 3.25∘F is less than 3.375∘F.
4. Neither, because Inga and Aileen had different measurements.
Answer: AILEEN’S THERMOMETER, BECAUSE IT HAS SMALLER INCREMENTS
Step-by-step explanation:
I did the test and the attachment below is a screenshot of my test and I got 100%
Aileen's thermometer has less uncertainty because it has smaller increments. Option A is correct.
Given that,
Inga and Aileen are measuring the temperature of frozen hydrogen. Inga is using a thermometer that has increments of 0.25∘F, and she gets a measurement of 3.25∘F. Aileen is using a thermometer that has increments of 0.125∘F, and she gets a measurement of 3.375∘F.
All over the world, most things are in use as of common quantity, so people all over the world agree that they have to follow a common system of measurement and that the common system of measurement is called standard measurement.
Here,
Aileen's thermometer has a smaller increment than Inga's thermometer,
Because of the smaller increments, it has more chances to give precise measurements and less uncertainty.
Thus, Aileen's thermometer has less uncertainty because it has smaller increments. Option A is correct.
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After a 40% discount, the cost of a sofa is $471.00. What was the original cost of the sofa? NEED HELP ASAP
Answer: $659.40
Step-by-step explanation: You start with 471.00 X 0.4 which equals $188.40. So then you add $471.00 and $188.40 and you get $659.40!
The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
80% = $471
100% = $588.75
The original cost of the sofa is $588.75
What is a percentage?The percentage is calculated by dividing the required value by the total value and multiplying it by 100.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Original cost in percentage = 100% ____(1)
Cost after 40% discount = $471
This can be written as,
80% = $471 _____(2)
From (1) and (2) we get,
80% = 471
Multiply 100/80 on both sides,
100/80 x 80% = 100/80 x 471
100% = $588.75
Thus,
80% = $471
100% = $588.75
The original cost of the sofa is $588.75
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So the question is pythagorean triple
Please and Thanks
Answer:
7) a = 10 / b = 5
8) x =
[tex]6 \sqrt{3} [/tex]
y =
[tex]3 \sqrt{3} [/tex]
Answer:
12
Step-by-step explanation:
jayfeather
What is the surface area of the cylinder
A. 80nft2
B. 112nft2
C. 88nft2
D. 96nft2
Shemika practices basketball for 2 hours each day
Answer:
whats your questionnnnn..???
Step-by-step explanation:
490 divided by 5 = what is the sum
The sum of 490 divided by 5 is 98.
To find the sum of 490 divided by 5, we need to perform the division operation and then add up the quotient and the remainder, if any.
When we divide 490 by 5, we get a quotient of 98.
There is no remainder because 490 is evenly divisible by 5. So, the quotient is the whole number result of the division.
To find the sum, we add the quotient and the remainder, if any.
In this case, there is no remainder, so the sum is simply the quotient: 98.
Therefore, the sum of 490 divided by 5 is 98.
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which is the measure of
Answer:
The measure of what?
Step-by-step explanation:
post the question again and I will see if I can answer it
pls help im bad at math
Answer:
SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS
Step-by-step explanation:
Its SSS
Riley invested $150 in an account paying an interest rate of 1 % compounded daily.
Blake invested $150 in an account paying an interest rate of 1% compounded
continuously. After 5 years, how much more money would Blake have in his account
than Riley, to the nearest dollar?
Answer:
$5
Step-by-step explanation:
Be prepared!!! Help please!!!! What is 1/3x 3.14x6^2x11 equal????
kevin and jenny each use 12 cups of water to make a plaster. who will make more plaster?
Answer:
Students solve problems by comparing different ratios using two or more ratio tables. ... If you used ratios to compare, what do the ratios mean in the context of this ... Laredo makes his juice by combining three cups of water for every one cup of ... Milton's Juice. Water. JC. Total. Water. JC. Total. Water. JC. Total. 12. 2. 14. 15.
Step-by-step explanation:
Which inequality is graphed in the coordinate plane
it is B
im not sure what else to say but my answer has to be 20 words or something
Find the area of a square with the side lengths of (1/2x+2)
Answer: There are no like terms
Step-by-step explanation:
5(2x+7) HELP ASAP PLS
Answer:
45x
Step-by-step explanation:
Plz mark brainliest
Kathy went to the store to buy school clothes. She had a store credit for
$29.58. If she buys 4 shirts that each cost the same amount and spends a
total of $42.22 after the store credit was taken off, what was the price of
each shirt?
Answer:
$17.95
Step-by-step explanation:
could be wrong but add the store credit to the amount she had to pay and then divide it by the amount of shirts bought, 4. also some expensive asz shirts.
What is the circumference of a circle with a diameter of 8 feet? Use 3.14 for
TT.
d = 8 ft
Answer:
25.12ft
Step-by-step explanation:
circumference = TT d
3.14 x 8 = 25.12 ft
You expected to walk 80 km in a day. You walked only 75 km. What was the percentage error?
596
6.25%
6.6796
93.3396
Answer:
Um my answer is 6.66666666667, so you could use this to help you (sorry i didn't get actual answer)
Step-by-step explanation:
Write an equation (the bottom square on the left is 3/2 btw) I WILL GIVE BRAINLIST IF ANSWER IS RIGHT
There are 15 plums and 9 apples in a fruit bowl. What is the ratio of apples to plums?
Answer:
5:3
Tell me if I'm correct
Can someone please help
Answer:
each hamburger costs $3.50
Step-by-step explanation:
he spent $13 in total and bought one hot dog for $2.50 and 3 hamburgers but we don't know the price of one hamburger so we could represent it by the equaton,
2.50 + 3h = 13 now solve for x
-2.50 2.50
3h = 10.50
h=3.50
check:
2.50+3(3.50)=13
2.50+10.50=13
13=13
l=$45, P=$600, t=2 years What is the annual interest rate?
Answer:
The interest rate required to accumulate simple interest of $ 45.00 from a principal of $600.00 over 2 years is 3.75% per year.
Step-by-step explanation:
Given
l = $45
P = $600
t = 2 years
To determine
What is the annual interest rate = r = ?
Using the Simple Interest Formula
I = Prt
r = I/Pt
substituting l = 45, P = 600 and t = 2 years
r = 45 / ( 600 × 2 )
= 0.0375
converting r decimal to a percentage = 0.0375 * 100 = 3.75% per year
Thus, the interest rate required to accumulate simple interest of $ 45.00 from a principal of $600.00 over 2 years is 3.75% per year.
Simplify (n-1) + n
Easy.
Answer:
2n - 1
Step-by-step explanation:
you add the 2 ns to get 2n then you add the 1 to the equation to make
2n - 1
WILL MARK BRAINLIEST!!!
This is a continuation to the other question
Answer:
m=86 degrees
x=98 degrees
Step-by-step explanation:
1:
the angles of a triangle are 180
180-71-23=86
m=86
2:
the angles of a triangle are 180
180-52-30=98
x=98
hope this helps and is right!
Paula is the student council member responsible for planning an outdoor dance. Plans include hiring a band and buying and serving dinner. She wants to keep the ticket price as low as possible to encourage student attendance while still covering the cost of the band and the food.
Question 1: Band A charged $600 to play for the evening and Band B changers $350 plus $1.25 per student.
Write a system of equations to represent the cost of the two bands.
Answer:
Plans include hiring a band and buying and serving dinner. She wants to keep the ticket price as low as possible to encourage student attendance while still covering the cost of the band and the food. Question 1: Band A charged $700 to play for the evening and Band B changers $550 plus $1.50 per student.
Step-by-step explanation:
Which of the expressions below has a 4 in the ones place of the sum? Select all that apply.
A) 7.46 + 6.22
B) 134.5 + 121.8
C) 12.35 + 11.81
D) 91.45 + 13.23
Answer:
its C or D
Step-by-step explanation:
i think it's both !
.. ¿Cuál es la densidad de una sustancia, si 460 gr ocupa un volumen de 35 cm3?
- Determinar la presión ejercida por una fuerza de 12 N aplicada a una superficie de 1,5 m2
Answer:
fghdd rtttuyer rfggysset hhgfd ishrhr Keith ieuru
Simplify: 2(10) + 2(x - 4)
Answer:
2x+12
Step-by-step explanation:
Multiply the numbers
2*10+2(x-4)
Distribute
20+2x(x-4)
20+2x-8
Subtract the numbers
20+2x-8
12+2x
Rearrange terms
2x+12
Together, the areas of the rectangles sum to 30 square centimeters.
3 cm
2 cm
cm
y cm
1. Write an equation showing the relationship between 3 and y.
Type the equation in the box below.
I
Answer:
3x+2y
Step-by-step explanation:
Find the rectangles attached
Area of a rectangle = Length * Width
A = A1+A2
given
A = 30cm²
A1 = 3 * x
A1 = 3x
A2 = 2*y
A2 = 2y
Substitute
30 = 3x+2y
Hence the required equation is 3x+2y = 30
Answer: 3x + 2y = 30
Step-by-step explanation:
A = L x W
The sum of the rectangle is 30.
One angle is 3 and x, the other one is 2 and y.
Multiply 3 with x = 3x.
Multiply 2 with y = 2y
Then create your equation plugging in 30 as the answer to 3x + 2y
Monica deposits $100 into a savings account that pays a simple interest rate of 4.5%, Paul
deposits $200 into a savings account that pays a simple interest rate of 3.2%. Monica says that
she will earn more interest in 1 year because her interest rate is higher. Is she correct? Justify your
response.
Answer:
yes she is correct
Step-by-step explanation:
because in 1 year it will go up 4.5%