Answer:
285 words
Step-by-step explanation:
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 = 29 − 0.2x (for 0 ≤ x ≤ 145),
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.
QUICK HELP PLEASE!!
AABC has vertices A(0, 10), B(8, 11), and C(6,3). Which coordinate proof correctly
shows that AABC is a scalene triangle?
Answer: AC= 85 BC= 68 and AB=65 The sides of the triangle are all of different lengths which means that ABC is a scalene triangle.
Step-by-step explanation: A scalene triangle only has different lengths! :)
Please Help Me ASAP I Need Real Help
Find the angle measures. Justify your responses. Given: a||b, m∠6=128 Find: m∠1,m∠3
Answer:
Angle 1 = 52
Angle 3 = 52
Step-by-step explanation:
Use the theorems
Line b is a straight line which is 180 degrees.
Angle 5 plus angle 6 need to equal 180
Angle 5 = 180 - 128 = 52
Angle 1 is the same as angle 5 because they are located in the same place on a straight line.
Angle 1 = 52 degrees.
Angle 3 is a vertical angle to angle 1, which means they are identical so angle 3 is also 52 degrees.
Jenna bought a jacket for $85.75. Agnes spent 2.20 times as much on hers. How much did Agnes spend?
answer:
188.65
Step-by-step explanation:
Answer:
188.65
Step-by-step explanation:
if you do 85.75*2.20 because it says times so that means multiply.
What is the solution to the following system of equations?
4x + 2y = 18
x - y = 3
(-4,-1)
(1.4)
(-1,-4)
(4.1)
Answer:
(4,1)
Step-by-step explanation:
hope that can help!!
What is the Sum of (2n^−5n−6)+(−n^2−3n+11)?
Answer:
n^2-8n+5
Step-by-step explanation:
(9x-4y) x (-2) + (3x+2y)
Answer:(3x-2y)(3x+2y)
Step-by-step explanation:
IT is this one
Answer:[tex]-18x^{2} +8yx+3x+2y[/tex]
Step-by-step explanation:
Joshua was offered a job that paid a salary of $77,500 in its first year. The salary was set to increase by 2% per year every year.
If Joshua worked at the job for 5 years, what was the total amount of money earned over the 5 years, to the nearest whole
number?
Answer:
if you want it as dollars and cents it is $77.50 but in nearest whole number it would be 78 dollars
Step-by-step explanation:
step 1: multiply the 2 by 5 and you get 10%
step two: you put 10 over 100 and multiply 77,500
10/100 x 77,500/1= $77.50
but when you roung it off you get 78 dollars
Answer: joshua earned $403,313 over 5 years
Step-by-step explanation:
87= 5x - 13
(Worth 10 points)
Answer:
x=20
Step-by-step explanation:
87=5x-13
100=5x ( add 13 on both sides)
x=20 ( divide by 5 on both sides)
Hope this helps plz mark brainliest :D
If DB = 36 and AC = 3x - 3, what is the value of x?
Answer:
A.) 13
Step-by-step explanation:
Since DB =36, and AC is the same line, then AC = 36. The new equation is 36 = 3x - 3. Do inverse operation. Add 3 to both sides of the equation: 36+3=39 & -3+3=0. New equation is 39=3x. Finally divide. 39/3= 13.
Evaluate [tex]\frac{u}{z} +xy^3[/tex], for u = 18, x = 8, y = 10, and z = 2.
Use slope formula,m = StartFraction y 2 minus y 1 Over x 2 minus x 1 EndFraction, to find the slope of a line that passes through the points (–3, 8) and (4, –6). giving 100 points
Answer:y=-2x+11 hope this helps
Step-by-step explanation:
Answer:
y=-2x+11
Step-by-step explanation:
two step equation -5=d/4+3
Answer:
If you are looking for d the answer is -32.
Step-by-step explanation:
-5=d/4+3
-3 -3
(4)-8=d/4(4)
-32 =d
PLEASE HELP WHAT IS THE GREATEST INTEGER THAT ALWAYS DIVIDES THE DIFFERENCE OF SQUARES OF ANY TWO POSITIVE ODD INTEGERS PLEASEEEE
All basketballs at a sporting goods store were marked down 25% during the first week of a sale. During the third week, all remaining basketballs were marked down an additional 30%. If a basketball was originally $22, how much does it cost during the third week?
Answer:
selling price= $9.9
Step-by-step explanation:
Giving the following information:
During the third week, all remaining basketballs were marked down an additional 30%.
Original price= $22
To calculate the selling price in the third week, we need to use the following formula:
selling price= original price*(1 - markdown)
selling price= 22*(0.45)
selling price= $9.9
What is the LCD of 20 and 12?
Answer:
60
Step-by-step explanation:
What is y=4/5x+20 in standard form
Answer:
4x-5y=-100
Step-by-step explanation:
Answer:
y = 100
Step-by-step explanation:
Standard Form 1/5y-20=0
Which situations most likely involve the use of decimals? Choose more than one answer.
Counting the number of apples in a basket
Measuring a person's height in meters
Calculating the price of an item after tax
Predicting the next full moon
Comparing the batting averages of two baseball players
Estimating the weight of an elephant
Answer:
Estimating the weight of an elephant
Step-by-step explanation:
Put an elephant onto a large boat and the marker that the water rises to Minus the starting point
-2a + 3 = 30-12 what does that equal ?
Find the slope of each line
Answer:
The slope of the blue line is undefined
Step-by-step explanation:
This is because a vertical line cannot have a numerical value for it's slope. Also, there is no y-intercept
Steve made $50 raking leaves and $75 mowing lawns. He gave 60% of his earnings to his mother. How much did Steve give to his mother?
Answer:
Step-by-step explanation:
75+50= 125
125*60%= 75 to his mother.
Answer:
Steve gave $75 to his mother.
Thus, Steve gave $75 to his mother.
If there were 9 apples and John ate 8 of them, then went to the supermarket to buy another apple. How many apples does John have?
Answer:
1 apple
Step-by-step explanation:
9 apples - 8 apples, so there is one apple left, but it is not John's apple, and he goes to the store to buy one so now he has one. :)
can someone answer this pls
Sunscreen is priced at $6 per bottle plus 8% tax. If Tony purchases TWO bottles of sunscreen and pays with a $20 bill, how much change will he receive?
Answer: $9.20
Step-by-step explanation:10 x 1.08 = 10.80. 20 - 10.80 is 9.20.
the sum of a number and 6 is no less than 31
Answer:
n + 6 > 31
Step-by-step explanation:
Plssss helppppp?????
Answer:
B and D
Step-by-step explanation:
0.6D & d + 0.6d
HOPE THIS HELPS
PLZZ MARK BRAINLIEST
Hiya! Does anyone know this? Plz help!
I think it is Ben
i had to do dis cuz of mininum 20 characters
Answer: Ben
Step-by-step explanation: Because rational numbers can be described as fractoins deicmals and repeating numbers
PLEASE HELP 20 POINTS. Select Yes or No to indicate whether a zero must be written in the dividend to find the quotient.
1.4/0.05 {select}
2.88/0.6 {select}
2.61/0.3 {select}
Answer:
Yes
Step-by-step explanation:
The cost of two pants and four shirts is $55.85. If a pant costs $7.25 more than a shirt, find the cost of a pant and a shirt. Estimate to the nearest whole number.
Cost of a shirt is $6 and cost of a pant is $13
Cost of a shirt is $7 and cost of a pant is $14
Cost of a shirt is $8 and cost of a pant is $14
Cost of a shirt is $7 and cost of a pant is $13
Answer:
B
Step-by-step explanation:
55.85 divided by 7.25 is 7. something sooooo if pants cost 7 dolars more thats 14
The cost of a shirt is $7 and the cost of a pant is $14.
The answer is option B.
What is an example of a word problem?
Word problems normally include mathematical modeling questions, where records and information approximately a positive machine is given and a student is needed to expand a model. For example, Jane had $5.00, then spent $2.00. How much does she have now?
Learn more about Word problems here: brainly.com/question/13818690
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