Answer:
Both prices should be set to #25.
The maximum revenue is #4375
Step-by-step explanation:
Given
[tex]q_1 = 150-2p_1-p_2[/tex]
[tex]q_2 = 200-p_1-3p_2[/tex]
Start by calculating the total revenue (R):
[tex]R = p_1q_1 + p_2q_2[/tex]
[tex]R = p_1(150-2p_1-p_2) + p_2(200-p_1-3p_2)[/tex]
[tex]R = 150p_1-2p_1^2-p_1p_2 + 200p_2-p_1p_2-3p_2^2[/tex]
Collect and solve like terms
[tex]R = 150p_1+ 200p_2-2p_1^2-2p_1p_2 -3p_2^2[/tex]
Differentiate with respect to pi and to p2, respectively
[tex]\frac{dR}{dp_1} = 150 -4p_1 - 2p_2[/tex]
[tex]\frac{dR}{dp_2} = 200 -2p_1 - 6p_2[/tex]
Equate both to 0, to get the critical point
[tex]150 -4p_1 - 2p_2 = 0[/tex]
[tex]200 -2p_1 - 6p_2 = 0[/tex]
Solve for p1 in [tex]150 -4p_1 - 2p_2 = 0[/tex]
[tex]4p_1 = 150 - 2p_2[/tex]
[tex]p_1 = 37.5 - 0.5p_2[/tex]
Substitute [tex]p_1 = 37.5 - 0.5p_2[/tex] in [tex]200 -2p_1 - 6p_2 = 0[/tex]
[tex]200 - 2(37.5 - 0.5p_2) - 6p_2 = 0[/tex]
[tex]200 - 75 - p_2 - 6p_2 = 0[/tex]
[tex]125 - 7p_2 = 0[/tex]
[tex]-7p_2 =-125[/tex]
[tex]p_2 = 25[/tex]
Substitute [tex]p_2 = 25[/tex] in [tex]p_1 = 37.5 - 0.5p_2[/tex]
[tex]p_1 = 37.5 - 0.5 * 25[/tex]
[tex]p_1 = 37.5 - 12.5[/tex]
[tex]p_1 = 25[/tex]
So, we have:
[tex]p_1 = p_2 = 25[/tex]
This implies that the prices should be set to #25.
The maximum possible revenue is:
[tex]R = 150p_1+ 200p_2-2p_1^2-2p_1p_2 -3p_2^2[/tex]
[tex]R = 150 * 25 + 200 * 25 -2 * 25^2 - 2 * 25 * 25 - 3 * 25^2[/tex]
[tex]R = 4375[/tex]
The maximum revenue is #4375
The maximum possible revenue is 4375.
How to calculate the revenue?From the information given, the following can be deduced:
Q₁ = 150 - 2P₁ - P₂
Q₁ = 150 - 2P₁ - P₂Q₂ = 200 - P₁ - 3P₂
The total revenue will be:
R = P₁Q₁+ P₂Q₂
R = P₁(150 - 2P₁ - P₂) + P₂(200 - P₁ - 3P₂)
R = 150P₁ + 200P₂ - 2P₁² - 2P₁P₂ - 3P₂²
To maximize, differentiate it in both the direction of P₁ and P₂.
d/dP₁ = 150 - 4P₁ - 2P₂
d/dP₂ = 200 - 2P₁ - 6P₂.
Solving for P₁ goes thus:
4P₁ = 150 - 2P₂
Divide through by 4
P₁ = 37.5 - 0.5P₂
Since 200 - 2P₁ - 6P₂ = 0
200 - 2(37.5 - 0.5P₂) - 6P₂ = 0.
P₂ = 25
Therefore, the revenue will be:
= 150P₁ + 200P₂ - 2P₁² - 2P₁P₂ - 3P₂²
= (150 × 25) + (200 × 25) - (2 × 25 × 25) - (3 × 25²)
= 4375
In conclusion, the revenue is 4375.
Learn more about revenue on:
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r − 38 = 9
please solve the equation
Answer:
r = 47
Step-by-step explanation:
r - 38 = 9
r- 38 + 38 = 9 + 38
simplify
r = 47
Answer:
[tex]r=47[/tex]
Step-by-step explanation:
[tex]r-38=9[/tex]
Add 38 to both sides of the equation:
[tex]r-38+38=9+38\\r=47[/tex]
r = 47 is your final answer.
When creating equations for our word problems, we must remember to...
A. write all equations in slope-intercept form.
B. make sure all equations are in the same form.
C. define all variables.
9514 1404 393
Answer:
C. define all variables
Step-by-step explanation:
Equations for word problems will depend on the problem. Not all of the equations will be linear equations. Even if they are, they are not necessarily easily written in any particular form, or easily solved when they are written in that form. The nature of the equations will depend on the problem.
One thing that must be done in any case is define all variables. It is usually a good idea to define the units of the variable(s) as well. Sometimes problems are posed with numbers in incompatible dimensions, or they may ask for an answer in dimensions different from those used in the given information. In order to avoid confusion and to be sure you have the desired answer, you need to make sure the variables and their dimensions are compatible with the solution process.
Find the perimeter of the figure to the nearest hundredth.
Answer:
perimeter of trapezium =sum of all sides
perimeter of trapezium =10cm+6cm+12cm+8cm
perimeter of trapezium =36cm
perimeter of semicircle =pi×r
perimeter of semicircle =3.14×6cm
perimeter of semicircle =18.84cm
perimeter of the figure =36cm+18.84cm=54.84cm
A circular railroad sign has a diameter of 20 inches. what is the area of the sign in square inches
Answer:
100[tex]\pi[/tex] (or about 314)
Step-by-step explanation:
So it's a circle, meaning that the formula for area is [tex]\pi r^{2}[/tex]. r= diameter divided by 2, so r=10. plug into equation and you get 100[tex]\pi[/tex].
314 is when you round pi to 3.14 and multiply by 100.
Consider the functions f(x) = x2 - 4x and
g(x) = (x - 2)2 + 3.
Which of the following statements are true? Select all that apply.
A)The graphs of f(x) and g(x) share the same axis of symmetry.
B)The graphs of f (x) and g(x) share the same y-intercept.
C)The graphs of f(x) and g(x) share the same
x-intercepts.
D)The graph of f(x) and g(x) open in the same direction.
The graph of f(x) is wider than the graph of g(x).
E)The vertical distance between the vertex of f(x) and the vertex of g(x) is 4 units.
Answer:
A, D
Step-by-step explanation:
graphed each function and looked at graphs to determine which statements were true
HELP NEED ANSWER ASAP!
Answer:
I am pretty sure the anwser is 7
Answer:
The median is 7.
Step-by-step explanation:
The median is 7 because, in a box plot, the line inside of the box is the median. That line is over 7 on the number line.
Solve the following percentage problem 85%of 40
Answer:34
85% of 40 = 34
Step-by-step explanation:85 percent of 40? = 34.
Answer:
34
Step-by-step explanation:
Find the surface area of the shape
Answer:
180
Step-by-step explanation:
Sebastian mixed 2 cups of red paint with 7 cups of blue paint to make his favorite shade of purple. Which ratio of red to blue paint will make the same shade of purple?
Answer:
10:35 is the ratio
Step-by-step explanation:
2 x 5 = 10
7 x 5 = 35
The formula for finding the area of a square that has a side length, s, is A = s2. If a square has an area of 40 square units,
what is the length of a side?
A. 2./10
B. 10.12
C. 20
Answer:
2./10
Step-by-step explanation:
It's simply by finding the square root of its area which is √40 giving 6.325 for an answer
If simplified by dividing each side with 3 then the answer would be 2./10
giving brainliest !!!!!!
Answer:
216
Step-by-step explanation:
6*6*6= 216
btw i am not using the formula for volume. 6*6 because you need the area of one side. then multiply that by 6 because there are 6 sides of a cube so 6*6*6=216
In AJKL, j = 55 inches, k = 51 inches and L=38°. Find the area of AJKL, to the
nearest square inch.
Answer:
863
Step-by-step explanation:
From reference sheet.
Plug in values.
Area≈863.465≈863
Evaluate and round.
Solve for x. Show your work:
2x+17+3x = 4x+3x+3
Answer:
The answer is 7
Step-by-step explanation:
2x+17+3x=4x+3x+3
5x+17=7x+3
5x-7x=3-17
-2x=-14
x=7
You are planning a survey of starting salaries for recent computer science majors. In the latest survey by the National Association of Colleges and Employers, the average starting salary was reported to be $60,038. 5 If you assume that the standard deviation is $4300, what sample size do you need to have a margin of error equal to $500 with 95% confidence
Answer:
A sample size of 285 is needed.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1 - 0.95}{2} = 0.025[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1 - \alpha[/tex].
That is z with a pvalue of [tex]1 - 0.025 = 0.975[/tex], so Z = 1.96.
Now, find the margin of error M as such
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
Standard deviation is $4300
This means that [tex]\sigma = 4300[/tex]
What sample size do you need to have a margin of error equal to $500 with 95% confidence?
A sample size of n is needed. n is found when M = 500. So
[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]
[tex]500 = 1.96\frac{4300}{\sqrt{n}}[/tex]
[tex]500\sqrt{n} = 1.96*4300[/tex]
[tex]\sqrt{n} = \frac{1.96*4300}{500}[/tex]
[tex]n = 284.1[/tex]
Rounding up
A sample size of 285 is needed.
solve the equation. -4/9 f= -3
Answer:
27/4
Step-by-step explanation:
Multiply both sides by 9/(-4).
9/−4 * −4/9 f = 9/−4 * −3
f = 27/4
The graph of a line has a slope of 2 and passes through the point (–6, –5). What is the equation of the line in point-slope form?
y – 5 = 2(x – 6)
y + 5 = 2(x + 6)
y – 6 = 2(x – 5)
y + 6 = 2(x + 5)
Answer:
it would be
B. y + 5 = 2(x + 6)
if there is a negative number and you are subtracting it turns positive
Step-by-step explanation:
An operation manager at an electronics company wants to test their amplifiers. The design engineer claims they have a mean output of 429 watts with a standard deviation of 10 watts. What is the probability that the mean amplifier output would be greater than 432.1 watts in a sample of 76 amplifiers if the claim is true
Answer:
0.0035 = 0.35% probability that the mean amplifier output would be greater than 432.1 watts.
Step-by-step explanation:
To solve this question, we need to understand the normal probability distribution and the central limit theorem.
Normal Probability Distribution:
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Mean output of 429 watts with a standard deviation of 10 watts.
This means that [tex]\mu = 429, \sigma = 10[/tex]
Sample of 76:
This means that [tex]n = 76, s = \frac{10}{\sqrt{76}} = 1.147[/tex]
What is the probability that the mean amplifier output would be greater than 432.1 watts?
This is 1 subtracted by the pvalue of Z when X = 432.1. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{432.1 - 429}{1.147}[/tex]
[tex]Z = 2.7[/tex]
[tex]Z = 2.7[/tex] has a pvalue of 0.9965
1 - 0.9965 = 0.0035
0.0035 = 0.35% probability that the mean amplifier output would be greater than 432.1 watts.
9. Complete the following equation using <,>, or =
100% _1
O A. >
O B. <
O C. =
Answer:
C. =
Step-by-step explanation:
Two ways to think about this problem:
1st way: 100% and 1 are all a whole, therefore, they are equal.
2nd way: 1=1/1. Multiply the denominator and the numerator by 100, 1/1=100/100=100%
Bella, Tia, and Ron participate in a trivia contest at a book shop. Tia scores 4 points, Ron scores 3 points, and Bella scores 2 points. Each player gets a number of paperback books equal to the square of the points he or she scores. What is the total number of books the players receive?
42 × 32 × 22
42 + 32 + 22
24 × 23 × 22
24 + 23 + 22
Answer:
4(2 on top) + 3(2 on top) + 2(2 on top)
Step-by-step explanation:
Solve for the area of the smaller
shape.
Round to the nearest TENTH.
What is the value of the expression: x2 + y2 + x - y
when x = -1 and y = 3
Question 1 options:
6
8
12
16
Answer: 6
Step-by-step explanation:
x^2+y^2+x-y
Put x=-1 and y=1
(-1)^2+(3)^2+(-1)-(3)
1+9-1-3
10-4
6
Someone actually help me w this ☝
Answer
Sorry If this is not correct, but I believe you keep the X varriable the same and multiply the Y varriable by 4. This means it will move to the right on the grid.
New coordinates: G(3,4) T(1,4) B(3, 20)
The mean midday temperature recorded in June in a city in South California is 36ºC, and the standard deviation is 3ºC. The number of days in the month of June is 30.
Assuming the data is normally distributed, the number of days in June when the midday temperature was between 39ºC and 42ºC is .
Answer:
About 4 days
Step-by-step explanation:
Convert 39 and 42 degrees C to a z score and then use the z-table
The number of days in June when the midday temperature was between 39°C and 42°C is equal to 4.0 days.
Given the following data:
Mean midday temperature = 36°C.
Standard deviation = 3°C.
How to determine the number of days in June?In order to determine the number of days in June when the midday temperature was between 39°C and 42°C, we would determine the z-score as follows:
Let the midday temperature be M.
P(39 < M < 42) = 1 - [P(M < 39) + P(M < 42)]
Evaluating, we have:
P(M < 39) = P(Z < [39 -36/3])
P(M < 39) = P(Z < [3/3])
P(M < 39) = P(Z < 1).
P(M < 39) = 0.84134.
P(M < 42) = P(Z < [42 -36/3])
P(M < 42) = P(Z < [6/3])
P(M < 42) = P(Z < 2)
P(M < 42) = 0.02275.
Substituting the parameters into the formula, we have;
P(39 < M < 42) = 1 - [P(M < 39) + P(M < 42)]
P(39 < M < 42) = 1 - [0.84134 + 0.02275]
P(39 < M < 42) = 1 - 0.86409
P(39 < M < 42) = 0.13591.
Now, we can determine the number of days in June when the midday temperature was between 39°C and 42°C:
No. of days = 0.13591 × 30
No. of days = 4.0 days.
Note: There are 30 days in the month of June.
Read more on z-scores here: https://brainly.com/question/4302527
#SPJ2
(-10) + 3 = 10 - 3 is true or false???
(-10) + 3 = -(10 - 3) = -7
10 - 3 = 7
-7 ≠ 7
FALSE
AABC is isosceles.
MZA = 48° and mZB = 4x + 4.
A
B
x= [?]
Pls help! This test determines if I take math 1 or 2 for 8th grade!!
Answer:
My best guess is D she can make 4 dozen cokies
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
it is B because for number A 1+1 =2 2>1.75. B= 1.5<175, c= 0.5 <1, d. 2>1.75
Jayla had some video games, and then she bought 4 more games. Now she has 10 games.
1) Write the equation that matches this situation.
2) Define the variable.
3) Find the solution.
Step-by-step explanation:
Jalya's video games = x
She bought four more = +4
Now what she has = 10
1. x+4=10
2. The variable x represents the unknown value of the video games Jayla had.
3. x+4=10(Group like terms)
x=10-4
x=6
A dictionary contains the following 8 words: to, many, joyous, birthday, wishes, happy, you, cake. What is the probability
of randomly generating the phrase happy birthday to you?
Answer:
not completely accurate but about 40%
Step-by-step explanation:
Answer:
40%
Step-by-step explanation:
since there are 8 words, do 8x5 which would be 40%
hope this helps!
please give me brainliest :)
Help pls this is my first question on here and I need help with this pls. I will give you the brainliest and a thanks!! :)) Can you do 1 and 4 thanks!! :)))
Answer:
1. 18.85in
4. 25.13m
Step-by-step explanation:
I got you
So to find the circumference of any circle we use the equation 2pi(r)
2(3.1415)(3)= 18.85in for the first one because radius is half of the diameter which is 6 so half of 6 is 3
For 4. 4m is actually the radius so just plug that into the equation 2pi(4)=25.13m
Naming with the vertex only won't work when there are multiple angles with the same vertex. True or False?