Given the demand and cost function shown below, calculate the profit maximizing quantity Q(P) 31.175-25P C(Q)-689Q 5075 QUESTION 5 Given the demand and cost function shown below, calculate the profit maximizing quantity Q(P)-2,314-89P C(Q)=12Q 13.54 QUESTION 6 Using the graph below, calculate the firm's profits at the profit maximizing output 196 168 154 140 126 112 84 70 56 42 28 14 23 46 69 92 115 138 261 194 207 230 253 Quantity ---MRMC-AC Price
Answers
Profit Maximizing Quantity (Q) is the output level at which a company generates the highest possible profit while maintaining its price and marginal costs. The formula for calculating the Profit Maximizing Quantity is MR = MC.In the first demand and cost function, the demand function is:
Q = 31.175-25P, where P is the price and Q is the quantity sold.
C(Q) = -689Q + 5075. Here, C(Q) is the cost function.We know that the marginal cost of the product (MC) equals the derivative of the cost function;
MC = C’(Q) = -689.
We also know that, since demand is a function of price and price is a function of quantity, we can use the chain rule to get the inverse demand function (P = P(Q)):
dP/dQ = dP/dQ * dQ/dP => 1/(-25) = dP/dQ => -0.04 = dP/dQ
We can use this relationship to obtain MR (marginal revenue) by multiplying both sides by P:
MR = P * (-0.04) = -0.04P.
The profit-maximizing quantity is determined by setting MR equal to MC:
MR = MC => -0.04P = -689 => P = 17225.
The inverse demand function (P = P(Q)) can be used to determine the quantity sold at the profit-maximizing price:17225 = 31.175-25Q => 25Q = -17193.825 => Q = -687.753
This solution is impossible because the quantity must be positive.
As a result, there is no profit-maximizing quantity in this scenario.In the second demand and cost function, the demand function is:
Q = -2,314-89P,
where P is the price and Q is the quantity sold.C(Q) = 12Q + 13.54. Here, C(Q) is the cost function.
The marginal cost of the product (MC) equals the derivative of the cost function;
MC = C’(Q) = 12.We also know that, since demand is a function of price and price is a function of quantity, we can use the chain rule to get the inverse demand function (P = P(Q)):
dP/dQ = dP/dQ * dQ/dP => 1/(-89) = dP/dQ => -0.01123595 = dP/dQ
We can use this relationship to obtain MR (marginal revenue) by multiplying both sides by P:
MR = P * (-0.01123595) = -0.01123595P.
The profit-maximizing quantity is determined by setting MR equal to MC:
MR = MC => -0.01123595P = 12 => P = -1066.13.
The inverse demand function (P = P(Q)) can be used to determine the quantity sold at the profit-maximizing price:-1066.13 = -2,314-89Q => 89Q = 1248.13 => Q = 14.
The profit-maximizing quantity (Q) is 14.
In the graph, we can see that the profit maximizing output is at 168.
To calculate the profit at the profit maximizing output, we need to find the point of intersection between the MR and MC curves and then multiply the quantity by the difference between the price (P) and average total cost (ATC) to get the profit.
The point of intersection in this case is approximately (168, 21).The price is 21 and the ATC is 10, therefore the profit is (21-10) * 168 = 1848. Answer: 1848
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Related Questions
Adi bought a bag for $25 and sold it at a loss of 10%. Find the selling price of the bag.
Answers
Answer:
The selling price of the bag is $22.5
Step-by-step explanation:
Buying Price = $25,
Selling Price = ?
Since they sold it at a loss of 10%,
So, they sold it for a price 10% less than the buying price,
or at 90% or 0.9 of the buying price,
so,
Selling Price = (0.9)(25) = $22.5
-2x + 4y = 12
5x - 2y = 10
To answer please type altogether with no spaces. For example if your answer is negative three positive four, type (-3,4)
Answers
Answer:
(4,5)
Step-by-step explanation:
-2x + 4y = 12
5x - 2y = 10
make them both set to y
4y = 2x + 12 -> y = 1/2x + 3
2y = 5x - 10 -> y = 5/2x - 5
since they're both equal to y, they are equal to each other
1/2x + 3 = 5/2x - 5
2x = 8
x = 4
plug it back in to get y
y = 1/2 (4) + 3
y = 5
The freshman class at Arlington High school is made up of 480 female students. This represents 65% of the freshman class. How many total students are freshmen?
Answers
The number of freshmen that are students is 738
How to calculate the number of freshmen that are students?
Let y represent the number of students that are freshmen
The freshmen class is made up of 480 female students
This number represents 65% of the freshmen class
Therefore the total number of students that are freshmen can be calculated as follows
y × 65/100= 480
65y/100= 480
Cross multiply both sides
65y= 480 × 100
65y= 48000
y= 48000/65
y= 738.4
≅ 738
Hence 738 students are freshmen
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Consider the following compound inequality.-24 <= 4x - 4 <= -12a) Solve the inequality for x.b) Graph the compound inequality.c) Enter the solution in interval notation.
Answers
Solution for given inequality is \(-5\leq x\leq -2\)
or \(x\) ∈ [ -5 , -2]
a.) Solve -24 <= 4x - 4 <= -12
Case I :
-24 <= 4x - 4
\(-24 + 4\leq 4x\)
\(-20 \leq 4x\)
\(\frac{-20}{4} \leq x\)
\(-5\leq x\) ........ (I)
Case II :
4x - 4 <= -12
\(4x\leq -12+4\)
\(4x\leq -8\)
\(x\leq \frac{-8}{4}\)
\(x\leq -2\) ......................(II)
combining (I) and (II) we get,
\(-5\leq x\leq -2\)
b). graph of
\(-5\leq x\leq -2\) , refer the attachment
c). Solution in interval
\(x\) ∈ [ -5 , -2]
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What is the value of f?
−1/8f−3/4−1/4f=11
Answers
Answer:
equals x cuz x is in definite number
Step-by-step explanation:
four years later, the same two hundred students were asked if they would consider themselves religious, yes or no. the scientist decided to perform mcnemar's test. the data is below. what is the test statistic?
Answers
The test statistic for McNemar's test, based on the given data, is approximately 1.19.
To calculate the test statistic for McNemar's test, we need to determine the values for the cells with in the After College contingency table. These values represent the cases where students' religious beliefs have changed.
Before College
Yes No
Yes 110 30
No 38 22
To find the test statistic, we use the formula:
Test Statistic = ((b-c) - 1)²/b+c
Where:
"b" is the number of students who changed from "Yes" to "No" (30 in this case)
"c" is the number of students who changed from "No" to "Yes" (38 in this case)
Plugging in the values, we have:
Test Statistic= ((30 - 38 ) -1)²/30 +38
Simplifying:
Test Statistic = 1.19
Therefore, the test statistic for McNemar's test, based on the given data, is approximately 1.19.
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The complete question is :
A scientist was interested in studying if students religious beliefs change as they go through college. Two hundred randomly selected students were asked before they entered college if they would consider themselves religious, yes or no. Four years later, the same two hundred students were asked if they would consider themselves religious, yes or no. The scientist decided to perform McNemar's test. The data is below. What is the test statistic?
After College
Before College Yes No
Yes 110 30
No 38 22
Using trigonometry, work out the size of angle x in
the right-angled triangle below.
Give your answer in degrees to 1 d.p.
5.3 m
8.2 m
x
Answers
Answer:
40.3°
Step-by-step explanation:
sin x/ (5.3) = sin 90/ (8.2)
sin x = (5.3 sin 90) / 8.2
= 5.3/8.2
x = arcsin (5.3/8.2)
= 40.3° to 1 dp
The measure of angle x using Trigonometry is 40.263215° or 40.3.
Trigonometry is a branch of mathematics that deals with the study of relationships involving the angles and sides of triangles. It is especially useful in understanding the properties and behavior of right-angled triangles.
Sine ratio is defined as the ratio of the length of the side opposite an angle to the length of the triangle's hypotenuse.
From the figure,
Perpendicular = 5.3 m
Hypotenuse = 8.2 m
Using Trigonometry
sin x = P / H
sin x = 5.3/ 8.2
sin x = 0.6463
Using Inverse Trigonometry
x = \(sin^{-1}\)(0.6463)
x= 40.263215°
Thus, the measure of angle x is 40.3.
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Which statement is true of table A and table B shown below?
Table A represents a function because there is only one output for
each input value.
Table B represents a function because there is only one output for
each input value.
Table A represents a function because there is only one input for each
output value.
Table B represents a function because there is only one input for each
output value.
Answers
Table A represents a function, but Table B does not represent a function.
What is a function?
A unique kind of relation called a function is one in which each input has precisely one output. In other words, the function produces exactly one value for each input value. The graphic above shows a relation rather than a function because one is mapped to two different values. The relation above would turn into a function, though, if one were instead mapped to a single value. Additionally, output values can be equal to input values.
A function or mapping is described as a collection of pairs of x and y that are ordered such that given different values of x, there will also be different values of y, or vice versa. For instance, the function x=y+2 yields a different x for every different value of y, while yielding the same x value for every single different value of y. We obtain two distinct x for two distinct ys, thus we can refer to this as a function at that point.
As, each element of X is associated with unique element of Y, so this is a function.
Table A
X Y
3 1
2 0
1 0
As, each element of X is associated with a unique element of Y, so this is a function.
Table B
X Y
3 -2
5 1
5 2
Hence, Table A represents a function, but Table B does not represent a function.
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on a survey, students must give exactly one of the answers provided to each of these three questions: $\bullet$ a) were you born before 1990? (yes / no) $\bullet$ b) what is your favorite color? (red / green / blue / other) $\bullet$ c) do you play a musical instrument? (yes / no) how many different answer combinations are possible?
Answers
There are 16 different answer combinations possible for the three questions.
For each question, there are a certain number of answer choices available. Let's analyze each question separately:
Were you born before 1990?" - This question has 2 answer choices: yes or no.
b) "What is your favorite color?" - This question has 4 answer choices: red, green, blue, or other.
c) "Do you play a musical instrument?" - This question has 2 answer choices: yes or no.
To find the total number of answer combinations, we multiply the number of choices for each question. Therefore, we have 2 * 4 * 2 = 16 different answer combinations.
For question a, there are 2 choices. For each choice in question a, there are 4 choices in question b, resulting in 2 * 4 = 8 combinations. For each of these 8 combinations, there are 2 choices in question c, resulting in a total of 8 * 2 = 16 different answer combinations.
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Which inequality represents the domain of the exponential piece?
a x>3
b x greater than or equal to -1
c x>1
d x less than or equal to -2
Answers
Using it's concept, it is found that the inequality represents the domain of the exponential piece is:
d) \(x \leq -2\).
What is the domain of a function?The domain of a function is the set that contains all possible input values.
Researching this problem on the internet, we have that the function is divided as follows:
For \(x \leq -2\), it has exponential behavior.For x > 2, it has polynomial behavior.Hence, for the domain of the exponential piece, option d is correct.
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Prepare a report answering the following three questions about the Stokes approximation and Oseen approximation.
[1] Briefly describe the two approximations.
[2] Interpret the difference between the results of the two approximations in terms of fluid dynamics.
[3] Give your opinion on the significance of the difference between the two approximations.
Answers
The Stokes approximation and Oseen approximation are methods used to determine the motion of fluid particles in a fluid dynamics problem.
The Stokes approximation applies to slow-moving fluid particles, where viscous forces are dominant, while the Oseen approximation applies to higher velocities, where convective forces are dominant..Oseen approximation: In this approximation, the equations governing the motion of fluid particles account for the convective forces in addition to the viscous forces.
This approximation is valid at moderate Reynolds numbers and is used when the viscous forces are still strong but not as dominant as in the Stokes approximation. The velocity of the fluid decreases less rapidly than in the Stokes approximation, and the approximation is valid for Reynolds numbers greater than one .The difference between the results of the two approximations lies in their range of applicability and the accuracy of their results.
The significance of the difference between the two approximations lies in their application to real-world problems. In fluid dynamics, it is essential to have accurate approximations to predict the behavior of fluid particles accurately. Therefore, choosing the appropriate approximation for the specific problem is critical. knowing the range of applicability of each approximation can help in determining the parameters for the problem.
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What value must b have in the function f(x)=x^4+bx^2+1 so that the function has at least one inflection point over the interval (1,2)?
Answers
The function f(x) = x^4 + bx^2 + 1 has an inflection point at x = 0,
What is the inflection point?
An inflection point of a function is a point on the graph of the function where the concavity (curvature) of the graph changes. In other words, an inflection point is a point where the curve switches from being concave up to concave down, or vice versa.
The function f(x) = x^4 + bx^2 + 1 has an inflection point at x = 0, because the concavity of the graph changes at that point. To find the value of b such that the function has at least one inflection point over the interval (1,2), we can set x = 1 and x = 2 in the function and solve for b.
If we set x = 1, we get the equation f(1) = 1 + b + 1 = 0. Solving for b, we find that b = -2.
If we set x = 2, we get the equation f(2) = 16 + 2b + 1 = 0. Solving for b, we find that b = -9.
Since the function has an inflection point at x = 0 for any value of b, it will have at least one inflection point over the interval (1,2) for any value of b.
Therefore, the value of b can be any real number.
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after a 40% reduction, you purchase a new computer monitor for $261. what was the price of the computer monitor before the reduction? a) first write an equation you can use to answer this question. use x as your variable and express any percents in decimal form in the equation. the equation is b) solve your equation in part [a] to find the original price of the computer monitor. answer: the original price of the computer monitor was dollars.
Answers
The computer monitor's original price was $435, after a 40% reduction, and it was purchased for $261.
a) The equation to answer this question is: 0.6x = 261, where x is the original price of the computer monitor before the reduction (since the price is reduced by 40%, you only pay 60% of the original price).
b) Solving the equation 0.6x = 261, we get:
x = 261/0.6
x = 435
Therefore, the original price of the computer monitor was $435.
To find the original price of a computer monitor that had a 40% reduction and was purchased for $261, we can use the equation 0.6x = 261, where x represents the original price. Solving for x, we divide both sides by 0.6, giving us x = 435. Therefore, the original price of the computer monitor was $435.
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5) A firm has $30,000 in a bank account at the beginning of the year. Interest will be paid at a rate of 2% at the end of the year. How much interest will the firm receive for the year?
Answers
Answer:
10%
Step-by-step explanation:
10% i think
what is the smallest three digist number divisible by the first three prime numbeers and the first three composite numberse
Answers
The smallest three-digit number divisible by the first three prime numbers (2, 3, and 5) and the first three composite numbers (4, 6, and 8) is 120.
The first three prime numbers are 2, 3, and 5. The first three composite numbers are 4, 6, and 8. In order for a number to be divisible by all six of these numbers, it must be divisible by their least common multiple (LCM).
The LCM of 2, 3, 5, 4, 6, and 8 is 120. Therefore, the smallest three-digit number divisible by the first three prime numbers and the first three composite numbers is 120.
Here is a more detailed explanation of how to calculate the LCM:
Find the prime factorization of each number.
Find the highest power of each prime factor.
Multiply the prime factors together, using the highest power for each factor.
The prime factorization of 2 is 2^1.The prime factorization of 3 is 3^1.The prime factorization of 5 is 5^1.The prime factorization of 4 is 2^2.The prime factorization of 6 is 2^1 * 3^1.The prime factorization of 8 is 2^3.The highest power of 2 that appears in any of the prime factorizations is 2^3.
The highest power of 3 that appears in any of the prime factorizations is 3^1.
The highest power of 5 that appears in any of the prime factorizations is 5^1.
Therefore, the LCM of 2, 3, 5, 4, 6, and 8 is 2^3 * 3^1 * 5^1 = 120.
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15
FY
In the diagram, mZCOE= 55°. If m22=2x and m23=x+10, what is the measure of angle 2?
30
45
BAI
60
E
HELP ASAP
Answers
Answer:
So here is how we are going to get the measure of angle 2.
Since given that angle COE measures 55°, we will equate m∠2 = 2x and m∠3 = x+10 with 55. So, 55 = 2x + x + 10
55 = 3x + 10
55-10 = 3x
45 = 3x << divide both sides by 3 and the result is
15 = x
So now that we know x, we can now solve for angle 2.
m∠2 = 2x
m∠2 = 2(15)
m∠2 = 30°
I hope that this is the answer that you are looking for
Cate and Elena were playing a card game. The stack of cards in the middle had 25 cards in it to begin with.
Cate added 8 cards to the stack. Elena then took 11 cards from the stack. Finally, Cate took 6 cards from
the stack. How many cards were left in the stack?
Answers
Answer:
16
Step-by-step explanation:
25 + 8 = 33
33 - 11 = 22
22 - 6 = 16
Evaluate Fonctions (Level 1)
Given g(x) = -3x + 3, find g(-2)
Answers
Answer:
g(-2) = 9
Step-by-step explanation:
g(x) = -3x + 3
g(x) = g(-2)
g(-2) = -3(-2) + 3
g(-2) = 6 + 3
g(-2) = 9
determine the level in decibels of a sound that has an intensity I = 10^-6 watts/cm2
Answers
Answer:
The level in decibels is 100.
Step-by-step explanation:
The intensity level in decibels (β) can be found using the following equation:
\( \beta = 10log(\frac{I}{I_{0}}) \)
Where:
I: is the intensity = 10⁻⁶ W/cm²
I₀: is the reference intensity = 10⁻¹² W/m²
First, we need to convert the unit of the given intensity from W/cm² to W/m².
\( I = 10^{-6} \frac{W}{cm^{2}}*\frac{(100 cm)^{2}}{1 m^{2}} = 10^{-2} W/m^{2} \)
Hence, the level in decibels is:
\( \beta = 10log(\frac{10 ^{-2} W/m^{2}}{10^{-12} W/m^{2}}) = 100 dB \)
Therefore, the level in decibels is 100.
I hope it helps you!
You need to show your understanding of Trigonometry by creating AND answering questions. You need to include a DIAGRAM as part of either the question or the answer. All questions have to be unique and not the same as any question from your course booklet, other groups or the Internet.
The outcomes you have to create question & answers for will be available to you in Tutorial B.
For each task please
• Write all group member's names and student numbers at the start of your page.
• Number and label your responses clearly
• Create a question
• Provide a sample answer (or two).
• Include a diagram in either the question or the
Answers
The ladder reaches approximately 8.66 meters up the building.
Guidelines for creating trigonometry questions and answers with diagrams:1. Identify the concept or outcome that needs to be assessed. This could be finding missing sides or angles of right triangles, using trigonometric ratios, solving word problems involving trigonometry, etc.2. Create a context or scenario that will require the use of trigonometry. This could be a real-life situation, a geometric problem, or a word problem.3. Draw a diagram that represents the situation or problem. Label the sides and angles of the triangle and any other relevant information.4. Write a question that asks the student to apply trigonometry to solve the problem. The question should be clear and specific, and should indicate what the student is expected to find.5. Provide a sample answer that shows the step-by-step process of solving the problem. The answer should be clear and easy to follow, and should include all relevant formulas and calculations.6. Include a diagram in either the question or the answer. The diagram should be neat, accurate, and labeled clearly. It should also be referenced in the answer so that the student can easily see how it relates to the problem being solved.Here's an example of a trigonometry question and answer with a diagram:Question:A 10-meter ladder is leaning against a building, making a 60-degree angle with the ground. How far up the building does the ladder reach?Answer:Step 1: Draw a diagram to represent the situation:Step 2: Identify the knowns and unknowns:Known:Angle A = 60 degreesSide a = 10 metersUnknown:Side b = ?Step 3: Select an appropriate trigonometric ratio to use. Since we are looking for the opposite side of a right triangle, we will use the sine ratio:Step 4: Solve for the unknown side:Step 5: Write the final answer: The ladder reaches approximately 8.66 meters up the building.
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Makayla leans a 26-foot ladder against a wall so that it forms an angle of 69 with the ground. What’s the horizontal distance between the base of the ladder and the wall?
Answers
The horizontal distance between the base of the ladder and the wall is approximately 8.892 feet.
Here, we have,
To find the horizontal distance between the base of the ladder and the wall, we can use trigonometric functions.
In this case, the ladder forms an angle of 69 degrees with the ground. We can label this angle as θ.
We know the length of the ladder is 26 feet. We can label the horizontal distance as x.
Using trigonometric functions, specifically cosine, we have:
cos(θ) = adjacent/hypotenuse
cos(69) = x/26
To find x, we can rearrange the equation:
x = 26 * cos(69)
Using a calculator, we can calculate:
x ≈ 26 * 0.3420
x ≈ 8.892
Therefore, the horizontal distance between the base of the ladder and the wall is approximately 8.892 feet.
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There are 360 seals on a beach. Of them 9/20 pups. The rest are adult seals. How many seal pups are on the beach? What percent of the seals on the beach are pups?
Answers
Answer:
Step-by-step explanation:
There are 360 seals on a beach. Of them 9/20 pups. The rest are adult seals. How many seal pups are on the beach? What percent of the seals on the beach are pups?
4) Angles 3 and 6 are congruent. What would you use to prove those lines parallel? (pic below)A. Converse of Same-Side Interior Angles Theorem
B. Alternate Interior Angles Theorem
C. Converse of the Corresponding Angles Postulate
D. Converse of Alternate Interior Angles Theorem
Answers
Answer:
B?
Step-by-step explanation:
x^2-x-2=0 as a complete square
Answers
Answer:
\(x_1=2; x_2=-1\)
Step-by-step explanation:
The square term is \(x^2\) so we expect the complete square to be of the form \((x-a) ^2=x^2+2ax+a^2\).
Let's compare the first degree terms now: we have \(2ax\) on one side and \(-1x\) on the other. That would make \(a=- \frac12\). At this point we have still the second squared term, so we add and subtract \(\frac14 = (\frac12)^2\)
Our equation becomes:
\(x^2-x+\frac14 -\frac14-2 =0\\(x-\frac12)^2-\frac94=0\)
(the \(\frac94\) term comes from rewriting \(2= \frac84\) and adding the terms out of the bracket).
At this point it's just solving the equation:
\((x-\frac12)^2 = \frac94 \rightarrow x-\frac12=\pm\frac32\\x=\frac12\pm\frac32\\x_1=\frac42 = 2; x_2=\fra-\frac22=-1\)
For a ride on a rental scooter, Boris paid a $2 fee to start the scooter plus 12 cents per minute of the ride. The total bill for Boris's ride was $10.52 . For how many minutes did Boris ride the scooter?
Answers
Answer: 119 minutes
Step-by-step explanation:
find the sum of the coefficients in the polynomial $3(x^{10} - x^7 2x^3 - x 7) 4(x^3 - 2x^2 - 5)$ when it is simplified.
Answers
The sum of the coefficients in the simplified polynomial is -54.
Adding two integers always results in an integer, if the two integers are positive, their sum will be positive, if two integers are negative, they will yield a negative sum)
To find the sum of the coefficients of the simplified polynomial, first, distribute the constants and then combine like terms.
The given polynomial is:
\($3(x^{10} - x^7 2x^3 - x 7) 4(x^3 - 2x^2 - 5)$\)
Distribute the constants:
\($3x^{10} - 3x^7 - 6x^3 - 3x - 21 + 4x^3 - 8x^2 - 20$\)
Combine like terms:
\($3x^{10} - 3x^7 + (-6x^3 + 4x^3) + (-8x^2) + (-3x) + (-21 - 20)$\)
Which simplifies to:
\($3x^{10} - 3x^7 - 2x^3 - 8x^2 - 3x - 41$\)
Now, sum the coefficients:
\($3 - 3 - 2 - 8 - 3 - 41 = -54$\)
So, the sum of the coefficients in the simplified polynomial is -54.
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Twelve increased by four times a number is
negative 8. I need the equation and solution !!
Answers
x = a number
12 + 4x = -8
Subtract 12 from both sides
4x = -20
Divide both sides by 4
x = -5
Find an equivalent fraction for the decimal number. In your final answer, include all of your work.
-—
0.61
Answers
Natalia and her friends held a bake sale to benefit a local charity, friends sold 15 cakes on the first dayand 22 cakes on the second day of the bake saleThey collected $60 on the first day $88 on the second day Write an equation to represent the amount R Natalia and her friends raised after selling c cakes .
Please i need this asap it’s due in 15 minutes!! I will give brainliest to whoever gets it right first!!
Answers
write 3 × 20 sec=t as a word problem
Answers
Answer:
If you had a three person relay race and you all took 20 seconds each, how long did your race last? hope this will help :)