Answer:
a. The company's profit function P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26
b. The number of cars that must be sold in each market are 60 in America, also 60 in Europe and 80 in Asia.
Step-by-step explanation:
Note: This question is not complete and it has some errors in the figures used. The correct complete question is therefore provided before answering the question as follows:
An automobile manufacturer sells cars in America, Europe, and Asia, charging a different price in each of the three markets. The price function for cars sold in America is p = 27 − 0.2x (for 0 ≤ x ≤ 135), the price function for cars sold in Europe is q = 15 − 0.1y (for 0 ≤ y ≤ 150), and the price function for cars sold in Asia is r = 19 − 0.1z (for 0 ≤ z ≤ 190), all in thousands of dollars, where x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively. The company's cost function is C = 26 + 3(x + y + z) thousand dollars.
(a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.]
P(x, y, z) =
(b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and Pz equal to zero and solve. Assuming that the maximum exists, it must occur at this point.]
The explanation to the answers is now given as follows:
(a) Find the company's profit function P(x, y, z). [Hint: The profit will be revenue from America plus revenue from Europe plus revenue from Asia minus costs, where each revenue is price times quantity.]
p = price function for cars sold in America = p = 27 − 0.2x (for 0 ≤ x ≤ 135)
q = price function for cars sold in Europe = 15 − 0.1y (for 0 ≤ y ≤ 150)
r = price function for cars sold in Asia = 19 − 0.1z (for 0 ≤ z ≤ 190)
C = company's cost function = 26 + 3(x + y + z) = 26 + 3x + 3y + 3z
P(x, y, z) = profit function
x, y, and z are the numbers of cars sold in America, Europe, and Asia, respectively
Therefore, we have:
TR = Total revenue = px + qy + rz …………………………….. (1)
Substituting the relevant values into equation (1), we have:
TR = (27 − 0.2x)x + (15 − 0.1y)y + (19 − 0.1z)z
TR = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2
Also,
P(x, y, z) = TR – C ……………………………………… (2)
Substituting the relevant values into equation (2), we have:
P(x, y, z) = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2 – (26 + 3x + 3y + 3z)
P(x, y, z) = 27x – 0.2x^2 + 15y – 0.1y^2 + 19z – 0.1z^2 – 26 – 3x – 3y – 3z
P(x, y, z) = 27x – 3x +15y – 3y +19z – 3z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26
P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26 ……………….. (3)
Therefore, the company's profit function P(x, y, z) = 24x +12y +16z – 0.2x^2 – 0.1y^2 – 0.1z^2 – 26.
(b) Find how many cars should be sold in each market to maximize profit. [Hint: Set the three partials Px, Py, and Pz equal to zero and solve. Assuming that the maximum exists, it must occur at this point.]
As indicated in the question, the number cars that should be sold in each market to maximize profit can be calculated by deriving the three partials Px, Py, and Pz from the profit function P(x, y, z), i.e. equation (3) in part a above, and set equal to zero and then solve as follows:
In America
From equation (3), we have:
Px = 24 – 0.4x = 0
Therefore, we have:
24 – 0.4x = 0
24 = 0.4x
x = 24 / 0.4
x = 60
In Europe
From equation (3), we have:
Py = 12 – 0.2y = 0
Therefore, we have:
12 – 0.2y = 0
12 = 0.2y
y = 12 / 0.2
y = 60
In Asia
From equation (3), we have:
Pz = 16 - 0.2z = 0
Therefore, we have:
16 - 0.2z = 0
16 = 0.2z
z = 16 / 0.2
z = 80
Based on the above calculations, the number of cars that must be sold in each market are 60 in America, also 60 in Europe and 80 in Asia.
This is for my lil sister
Answer: yes
Step-by-step explanation:
Answer:
9
Step-by-step explanation:
Gloria subscribes to the Webtime Internet Service. Webtime charges a $9.99 monthly service fee plus $1.50 per hour for Internet access. Last month's bill was $ 36.99. How many hours did Gloria use the Internet last month?
Answer:
18 hours
Step-by-step explanation:
Let the number of hours used to represented by x
Gloria subscribes to the Webtime Internet Service. Webtime charges a $9.99 monthly service fee plus $1.50 per hour for Internet access.
Total bill = $9.99 + $1.50 × x
= 9.99 + 1.5x
Last month's bill was $ 36.99.
Hence,
9.99 + 1.5x = 36.99
Collect like terms
1.5x = 36.99 - 9.99
1.5x = 27
x = 27/1.5
x = 18 hours
The number of hours that Gloria used the Internet last month is 18 hours
can anyone help me with this
Answer:
I only know how to do the LCM but thats it sorry
Step-by-step explanation:
I got this from the internet sorry if it dosen't help
LCM(84,90) = 1260
Answer:
HCF = 2 * 3
LCM = 2 *2 * 3 * 3 * 5 * 7
Step-by-step explanation:
A) 84 = 2 * 2 * 3 * 7
90 = 2 * 3 * 3 * 5
HCF = 2 * 3
B) 84 = 2 * 2 * 3 *7
90 = 2 * 3 * 3 * 5
LCM = 2 *2 * 3 * 3 * 5 * 7
Is this function linear or nonlinear?
y=3x−5
nonlinear
linear
Answer:
linear
Step-by-step explanation:
Answer:
It is linear.
Step-by-step explanation:
A line passes through the points (3,15) and (6,18). Write a linear function rule in terms of x and y for this line.
Answer:
= x+12
Step-by-step explanation
h Uu e ouwe;come
-----------> Comment your Epic Games Name or Nintendo Switch friend code here so I can add you on Rocket Leauge!(Answer if your plat 3 or above in doubles)<-------------------
Answer:
daddys_angel_yt
Step-by-step explanation:
Answer:
Step-by-step explanation:
Ricardoconsort14 and RicardoOrtVill
3/4x + 11 - 5 1/2 + 1/4x
[tex] \frac{3}{4} x + 11 - 5 \frac{1}{2} + \frac{1}{4} x[/tex]
[tex]( \frac{3}{4} x + \frac{1}{4} x) + (11 - 5 \frac{1}{2} )[/tex]
[tex] (\frac{3x}{4} + \frac{x}{4} ) + (11 + - \frac{11}{2} )[/tex]
[tex]( \frac{(3x + x)}{4} ) + ( \frac{22}{2} - \frac{11}{2} )[/tex]
[tex] \ \frac{4x}{4} + \frac{11}{2} [/tex]
[tex]x + \frac{11}{2} [/tex]
यूदि एक वृत्त का परिमाप और क्षेत्रफल बरावर हो
तो उसकी त्रिज्या क्या होगी?
Answer:
I Can't understand your language !!!!!
Step-by-step explanation:
Please ask it in English Lol !!!!
A refrigerator costs $599. If the tax is 7.5%, the additional amount of money necessary to purchase the refrigerator is
$4.52
$44.93
$75.00
Answer:
44.93
Step-by-step explanation:
7.5 x 599 divided by 100 = 44.925 = 44.93
What is the solution to
6(2 - x)<-4x + 2?
Answer:
Solving [tex]6(2 - x)<-4x + 2[/tex] we get [tex]\mathbf{x>5}[/tex]
Step-by-step explanation:
We need to find solution of [tex]6(2 - x)<-4x + 2[/tex]
Solving the inequality:
[tex]6(2 - x)<-4x + 2[/tex]
Multiply 6 with terms inside the bracket
[tex]12-6x<-4x+2[/tex]
Subtracting 12 on both sides
[tex]12-6x-12<-4x+2-12\\-6x<-4x-10[/tex]
Adding 4x on both sides
[tex]-6x+4x<-4x-10+4x\\-2x<-10[/tex]
Divide both sides by -2 and the inequality will be reversed i.e < will be changes to >
[tex]\frac{-2x}{-2}>\frac{-10}{-2}\\\mathbf{x>5}[/tex]
So, after solving [tex]6(2 - x)<-4x + 2[/tex] we get [tex]\mathbf{x>5}[/tex]
19 1/2 - 14? please help me!
Answer:
19.5 is the exact form for 19 1/2 so minus 14 is 5.5 or 5 1/2 so your answer is 5 1/2
Step-by-step explanation:
Answer:
5.5Step-by-step explanation:
19 1/2 - 14 = 5.5
I put a picture hopefully you can see it
Answer:
i think it might be the first or third one
Step-by-step explanation:
Jane is cooking in her recipe indicates that she should add several spices she needs to add 1/2 of a teaspoon of salt, 1 1/4 teaspoons of Orégano 3/4 of a teaspoon of basil in half as much pepper as salt. What is the total number of teaspoons of spices in the dish express the answer as a decimal
Answer: total number of teaspoons of spices in the dish =3.25 teaspoons
Step-by-step explanation:
Step 1
Listing the spices and their quantities , we have
Salt = 1/2 teaspoon
Orégano =1 1/4 teaspoon =5/4 teaspoons
Basil = 3/4 teaspoon
Pepper= in half as much pepper as salt -- This means that the quantity of pepper should be 50% more in quantity than salt
Therefore quantity of pepper = 50% x 1/2 = 0.5 x 0.5= 0.25
0.25 + 1/2 = 0.25 + 0.5 = 0.75 = 3/4 teaspoon of pepper.
Step 2
Adding the amount of spices we have
1/2 + 5/4+ 3/4+ 3/4 = 2+ 5+3+ 3/4 = 13/4 = 3 1/4 teaspoons of spices = 3.25 teaspoons of spices .
a recipe for trail mix calls for 50 grams of almonds for every 2 cups of oats. the line represents the relationship between the amount of almonds and the amount of oats needed to make trail mix according to this recipe. the point (1, 25) is on theine. what is the equation for this line? use the format y=kx
Answer:
The equation is: y=25x
Step-by-step explanation:
Linear Modeling
When two variables have a linear dependency, the relationship between them can be written as:
y=kx+b
Where k is the slope and b is the y-intercept. When b=0, then the relationship is called proportional, and the equation is:
y=k.x
For the question, we call y=grams of almond and x=cups of oats.
It's given for x=cups of oats, the recipe for trail mix calls for y=50 grams of almonds. Substituting into the equation:
50=k.2
Solving for k:
k=50/2=25
The final equation is:
y=25x
Note the point (1,25) is on the line, as required.
17. You roll two dice. How many ways can you roll a sum greater than 7 or a doubles?
Answer:
brainliest?
Step-by-step explanation:
Here is a list of numbers:
2.5, 2.8, 8.4, 1.1, 7.7, 6.3, 2.4 ,0.7 ,0.8 ,0.5
State the median.
2.4
The median is the middle number.
1. Put the numbers in order from smalllest to greatest
2. Pick the middle number
Select the statement that best describes the rates of the two cars
Answer: on the selected dots your answer should be that car 1 is traveling faster than car 2.
what is the answer for -4 (12)=
what is the answer
Answer:
-48
Step-by-step explanation:
12 x 4= 48 just add negative sign to 48.
Hope this helps :3
Answer:
-4(12) = -48
Step-by-step explanation:
Negative stay negative and 4 multiply by 12 is 48 from the multiplication table, therefore -4 multiply by 12 is -48.
You have a 12 inch by 14 inch picture that you frame. When you hung the picture, you found that the entire area is 261.44 in. What is the width of the frame?
Answer: 3.2 inches
Step-by-step explanation:
A student solved the problem below by first dividing 20 by 10. What mistake did the student make?
A baseball team has won 20 games and lost 10 games. What percent of the games did the team win?
Answer:
The student should have added 20 + 10 = 30 and then divide 30 by 3 to get 10 = 1/3 of 30 so the team won 2/3 or 66.6667%.
Step-by-step explanation:
16-2t=3/2t+9
Solve for t
Answer:
t=2
Step-by-step explanation:
16-2t=3/2t+9
you multiply everything with 2
32-4t = 3t+18
4t-3t=18-32
-7t=-14
t=2
Step 1: Minus the 16 from the 9
Step2: Multiply the 2t wirh the -2t.
Step 3: Divide -4 by -4
Does the table represent a proportional relationship? Show your work!
Which of the binomials below is a factor of this trinomial?
x^2 + 12x + 35
O A. x-5
O B. X+5
O C. x-1
O D. x+1
Answer:
B
Step-by-step explanation:
(x+7)(x+5)
what is the answer to this problem
4x²+3x+4x-1
Answer:
Step-by-step explanation:
4x^2+3x+4x-1 add like terms
4x^2+7x-1
If you use the quadratic formula the answer is -7±√65 /8
Let v = (v1, v2) be a vector in R2. Show that (v2, −v1) is orthogonal to v, and use this fact to find two unit vectors orthogonal to the given vector.
v = (21, 20)
Answer:
a. v.v' = v₁v₂ - v₁v₂ = 0 b. (20, -21)/29 and (-20,21)/29
Step-by-step explanation:
a. For two vectors a, b to be orthogonal, their dot product is zero. That is a.b = 0.
Given v = (v₁, v₂) = v₁i + v₂j and v' = (v₂, -v₁) = v₂i - v₁j, we need to show that v.v' = 0
So, v.v' = (v₁i + v₂j).(v₂i - v₁j)
= v₁i.v₂i + v₁i.(- v₁j) + v₂j.v₂i + v₂j.(- v₁j)
= v₁v₂i.i - v₁v₁i.j + v₂v₂j.i - v₂v₁j.j
i.i = 1, i.j = 0, j.i = 0 and j.j = 1
So, v.v' = v₁v₂i.i - v₁v₁i.j + v₂v₂j.i - v₂v₁j.j
= v₁v₂ × 1 - v₁v₁ × 0 + v₂v₂ × 0 - v₂v₁ × 1
= v₁v₂ - v₂v₁
= v₁v₂ - v₁v₂ = 0
So, v.v' = 0
b. Now a vector orthogonal to the vector v = (21,20) is v' = (20,-21).
So the first unit vector is thus a = v'/║v'║ = (20, -21)/√[20² + (-21)²] = (20, -21)/√[400 + 441] = (20, -21)/√841 = (20, -21)/29.
A unit vector perpendicular to a and parallel to v is b = (-21, -20)/29. Another unit vector perpendicular to b, parallel to a and perpendicular to v is thus a' = (-20,-(-21))/29 = (-20,21)/29
Which of the following transformations could have been used to map Figure A onto Figure B?
To map figure A onto figure B translation and dilation is used. The correct option is B.
What is dilation?Dilation is the process of increasing the size of an object while maintaining its shape. Depending on the scale factor, the object's size can be increased or decreased.
The process of changing the location of the image on the coordinate system will be known as the translation.
In the given image figure A is a parallelogram its size is increased or dilated and the figure is translated to the new location by using the translation.
Therefore, to map figure A onto figure B translation and dilation is used. The correct option is B.
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A baker uses chocolate with 75% cocoa for his famous cake. But his supplier delivered 100 lb of chocolate with 70% cocoa, so the baker needs to melt and mix the delivery with chocolate that has 90% cocoa. How much of the 90% chocolate should he use?
33 1/3 BTW i am from RSM too :)
33.33 lb of 90% cocoa cholcolate should be mixed.
What are percentages?A percentage is a number or ratio that can be expressed as a fraction of 100. If we have to calculate the percent of a number, divide the number by the whole and multiply by 100. Hence, the percentage means, a part per hundred. The word percent means per 100. It is represented by the symbol “%”
Given here: A baker has to mix 70% cocoa with 90% cocoa and he has 100 lb of the first chocolate.
let x lb of chocolate be mixed with 100 lb to give the 75 % chocolate variety
Thus, x×90%+100×70% / 90%+70% = 75%
0.9x+70 /x+100=0.75
0.9x+70=0.75x+75
0.15x=5
x=33.33
Thus 33.33 lbs of 90% cocoa should be mixed to get 75% cocoa
Hence, 33.33 lb of 90% cocoa cholcolate should be mixed.
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Question is: Andre solved an equation, but when he checked his answer he saw his solution was incorrect. He knows he made a mistake, but can’t find it. Where is andres mistake and what is the solution to the equation?
Answer:
he forgot to solve the -6 i hope thats right im srry if it isnt
Step-by-step explanation:
Answer:
-1=x
Step-by-step explanation:
They messed up on step 4. instead of -2x it should be -10x. When they switched -6 over to the opposite side they forgot to use the opposite symbol. They did 6-4 instead of 4+6.
Convert Y = -3/2X + 4 into standard form.
Kareem is a software salesman. His base salary is $2200, and he makes an additional $60 for every copy of Math is Fun he sells.
Let P represent his total pay (in dollars), and let N represent the number of copies of Math is fun she sells.
P = 2200 + 60N
Step-by-step explanation:
I gotcha covered!
