Answer:
your answer is A
Step-by-step explanation:
The weekly demand function for x units of a product sold by only one firm is
p = 800 − 0.5x dollars, and the average cost of production and sale is C(with a line on top) = 300 + 2x dollars.
(a) Find the quantity that will maximize profit.
(b) Find the selling price at this optimal quantity.
(c) What is the maximum profit?
Answer:
a) x = 798 is the quantity that maximizes the profit
b)po(x) = 401 $/unit
c)P(max ) = 636105 $
Step-by-step explanation:
The weekly demand function is equal to the price by unit and the Revenue function is weekly demand times quantity of units then:
R(x) = p(x) * x
R(x) = ( 800 - 0,5*x ) * x
R(x) = 800*x - 0,5*x²
The equation for the profit is:
P(x) = R(x) - C(x)
P(x) = 800*x - 0,5*x² - ( 300 + 2*x)
P(x) = 798*x - 0,5*x² - 300
a) P(x) = 798*x - 0,5*x² - 300
Taking derivatives on both sides of the equation:
P´(x) = 798 - x
If P´(x) = 0 then 798 - x = 0
x = 798 is the quantity that maximizes the profit
b) Selling price for the optimal quantity is:
p(x) = 800 - 0,5*x
p(x) = 800 - 0,5* 798
po (x) = 800 - 399
po(x) = 401 $/unit
c) Pmax = ?
P(x) = 798*x - 0,5*x² - 300 by subtitution of x = 798
P(max) = 636804 - 399 - 300
P(max ) = 636105 $
a) The quantity that will maximize profit is [tex]100 \ units[/tex].
b) The selling of at this optimal quantity is [tex]\[/tex][tex]750[/tex] per unit.
c) So, the maximum profit is [tex]\[/tex][tex]25000[/tex].
Demand Function:A demand function is a mathematical equation that expresses the demand for a product or service as a function of its price and other factors such as the prices of the substitutes and complementary goods, income, etc.
The given demand function,
[tex]P=800-\frac{1}{2}x[/tex]
So, the revenue function is,
[tex]R(x)=p.x\\R(x)=800-x-\frac{1}{2}x^{2}[/tex]
[tex]\Rightarrow[/tex]Average cost is
[tex]\bar{C}=300+2x[/tex]
So, the total cost function is,
[tex]C\left ( x \right )=\bar{C}.x \\ C\left ( x \right )=300x+2x^{2}[/tex]
a) Profit function:
[tex]P\left ( x \right )=R\left ( x \right )-C\left ( x \right ) \\ =800x-\frac{1}{2}x^{2}-300x-2x^{2} \\ P\left ( x \right )=500x-\frac{5}{2}x^{2}[/tex]
For maximum,
[tex]{P}'\left ( x \right )=0 \\ 500\left ( 1 \right )-\frac{5}{2}\left ( 2x \right )=0 \\ 500-5x=0 \\ x=100[/tex]
b) Selling Price:
[tex]P=800-\frac{1}{2}x \\ at \ x=100 \\ P=800-\frac{1}{2}\left ( 100 \right ) \\ =\$ 750[/tex]
c) Maximum Profit:
[tex]P\left ( x \right )=500x-\frac{5}{2}x^{2} \\ P\left ( 100 \right )=500\left ( 100 \right )-\frac{5}{2}\left ( 100 \right )^{2} \\ P\left ( 100 \right )=\$ 25000[/tex]
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There are approximately 330,000,000 cubic miles of water on Earth. A cubic mile is approximately 147,200,000,000 cubic feet. How much water is on Earth? Estimate using scientific notation
Answer: 4.8576 × 10^19 cubic feet of water.
Step-by-step explanation:
330m * 147.2b = 48 quintillion feet.
Answer:
5 x 10^19 ft^3
Step-by-step explanation:
What do you know about the slope of two parallel lines? *
They have the opposite sign of each other
They are reciprocals of each other
They have the same slope
They have negative reciprocal slopes
Answer:
same slope
Step-by-step explanation:
if it has the same slope then the you will know the two lines are parallel
hope this helps
brainliest?
Help pls it’s urgent
Answer:
d. -2
Step-by-step explanation:
they're telling you those lines are parallel there are specific knowns about the angles
since it's urgent I won't go into it, but PLS look it up it's super simple and makes sense
nonetheless this means angle 1 and angle 5 are the same value so we can set them equal
3x + 24 = 7x + 32
substract 32 from both sides
3x - 8 = 7x
substract 3x from both sides
-8 = 4x
divide 4 from both sides
-2 = x
What is the slope of y-5= 3x + 4?
Answer:
x=53
y=19
Step-by-step explanation:
3x + y-5
3(5)=15
15+y
how many inches of lumber are remaining?
Answer:
I can't really answer this question because there is no picture of actual question but 1 foot = 12 inches so for instance we could do 6 inches + 3 inches = 9 inches.
Step-by-step explanation: How we would solve this problem is simple.
6 + 3 = 9 if you have to turn this into a fraction it would be 9/12 = (3/4).
I need help on math
Which of the following is a true statement?
6/9 = 1/3
1/4 > 1/3
13/15 > 4/5
5/6 > 10/12
Answer:
13/15 > 4/5 is a true stament.
Step-by-step explanation:
The left side is 0.86 repeating turned into a decimal. which means 0.86 is greater than the right which the right is 0.8 turned into a decimal. which in this case this means that the given stament is always true.
How many times greater is the product of 4 x 300 than the product 4 x 30
Answer:
10 times bigger
Step-by-step explanation:
because if you do 4 times 300 thats 1200
and if you do 4 times 30 then you get 120
and 120 times 10 is 1200 so there you go.
HOPED THIS HELPED!!!!!!!!! :D
Two divers are swimming at different depths below sea level. One diver is at -25.5 ft. The other diver is at -40.75 ft. How far are the divers from each other?
Answer:
66.25 ft
Step-by-step explanation:
25.5 + 40.75
66.25
They are 66.25 feet away from each other.
Please let me know if I'm wrong!
Please help it would help me alot!!!
Answer: Total cost for 1 ride = $11. Total cost for 2 rides = $14. Total cost for 3 rides = $17. Total cost for 4 rides = $20. Total cost for 5 rides = $23
Step-by-step explanation:
A camera has a listed price of 873.95 before tax. If the sale taxes rate is 6.5, find the total cost of the camera with sales tax included. Round your answee to the nearest cent. As necessary.
Answer:
$930.76
Step-by-step explanation:
So if you move the decimal in the percentage over to the right by two then you have your sales tax rate in decimal form (0.065), you can then multiply that by the listed price and you'll have about 56.80675 so this number will be the sales tax price, then you may add this to the listed price and your answer will be 930.75675, then once you round up it will be $930.76.
Never Going To Give You Up never going to let you down never gonna run around baby nor desert you Rick roll..
Answer:
we're no strangers to love
Step-by-step explanation:
you know the rules, and so do I
How much mixed spice will she need for 6 spice
Answer:
who
Step-by-step explanation:
64 mi/h to ft/s HELP HELP HELP HELP NOW!!!! WILL PUT 5 STARS AND MARK BRAINLIEST!!!
Answer:
Multiply 64 x 5280
Step-by-step explanation:
You will get your answerhelloAnswer:
64 mi/h = 93.9 ft/s I have the answer guide
Which expression is equivalent to |-5| + |-3|
Answer:
5+3
Step-by-step explanation:
5+3
Answer:
5+3=8
Step-by-step explanation:
In a coordinate plane, plot the points and sketch
angle. Write the coordinates of a point that lies in the interior of the
angle and the coordinates of a point that lies in the exterior of the
angle.
A(-5,0)
B(-1,-4)
C(4,2)
Answer:
A.
Step-by-step explanation:
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. ex = 3 − 2x, (0, 1) The equation ex = 3 − 2x is equivalent to the equation f(x) = ex − 3 + 2x = 0. f(x) is continuous on the interval [0, 1], f(0) = _____, and f(1) = _____. Since f(0) < 0 < f(1) , there is a number c in (0, 1) such that f(c) = 0 by the Intermediate Value Theorem. Thus, there is a root of the equation ex = 3 − 2x, in the interval (0, 1)
Answer:
[tex]f(0)=-2\\f(1)=e-1[/tex]
Step-by-step explanation:
According to intermediate value theorem, if a function is continuous on an interval [tex][a,b][/tex], and if [tex]k[/tex] is any number between [tex]f(a)[/tex] and [tex]f(b)[/tex], then there exists a value, [tex]x=m[/tex], where [tex]a<m<b[/tex], such that [tex]f(m)=k[/tex]
In the given question,
Intermediate Value Theorem is used to show that there is a root of the given equation in the specified interval.
Here,
[tex]f(x)=e^x-3+2x[/tex]
Put [tex]x=0[/tex]
[tex]f(0)=e^0-3+2(0)=1-3+0=-2[/tex]
Put [tex]x=1[/tex]
[tex]f(1)=e^1-3+2(1)=e-3+2=e-1[/tex]
A proposed change in income tax suggests charging 20% on a person's income up to $30,000 and then 40% on any
income above that. If a person has an income of $47,000, what will be their income tax under the proposal?
Give your answer in dollars to the nearest dollar. Do not include commas or the dollar symbol in your answer.
Provide your answer below
Answer:
If you get tax you should know the details of the what the tax is FOR
Step-by-step explanation:
Not enough details in question
Answer:
Step-by-step explanation:
Since the person earns over $30,000, they will be charged 20% on $30,000 plus 40% on ($47,000−$30,000)=$17,000. Hence the total amount of tax that they'd need to pay under the proposal is
Total Income Tax=$30,000×20%+$17,000×40%=$30,000×20100+$17,000×40100=$6,000+$6,800=$12,800.
PLZ HELP !!
Max deposited $1,300 into an account that pays 4.5% interest, compounded daily. At end of six years he has a balance of ?
Answer:
The final balance is $1,692.94.
The total compound interest is $392.94.
Step-by-step explanation:
1,300 x 0.045=___ x 6
How can you use a number line to find the sum of -8 and 9?
Answer:
The answer is 1
Step-by-step explanation:
If you look at the number line and start counting from -8 and count 9 to the right then the number that you end on is the answer.
A rectangle has a length of 2x+1 and a width of 3x-2.
Write an expression for the area of the rectangle.
Answer:
(2x+1)x(3x-2)
Step-by-step explanation:
area of rectangle = length * width
length = 2x+1
width = 3x-2
area = (2x+1) x (3x-2)
16B+3.5W = 22 Antoine bikes part of the way on a 22 mile trail and walks the rest of the way. If he spends B hours biking and W hours walking, the trip is modeled by the equation shown above. What is the meaning of the 16B in the equation?
Answer:
Antoine bikes for 16B miles before starting his walk.
Step-by-step explanation:
16 is that speed which is covered in B hours by bike by Antoine
What is speed?Speed is defined as The rate of change of position of an object in any direction. Speed is measured as the ratio of distance to the time in which the distance was covered. Speed is a scalar quantity as it has only direction and no magnitude.
Speed = [tex]\frac{distance}{time}[/tex]
Given,
16B+3.5W = 22 an equation in which B is time covered by bike and W is time covered by walk
Antoine travels partially by bike and partially by walk, and total covered 22
That means 16B is the distance covered by bike, and 16 is its speed.
Hence, 16 is that speed which is covered in B hours by bike.
Learn more about speed:
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PLEASE HELP! 6TH GRADE MATH please write done what number you're doing
Answer:
# 10 is 4/3 or 1 and 1/3
#11 is 4/10 or 2/5
#12 is 2 and 3/4
#13 is 36/12 or 3 and 1/12
Step-by-step explanation:
i am not 100% sure on #13 btw
hope this helped!
p.s it would be cool if you gave me brainliest.
Answer:
Hey your answers on there are correct.
Step-by-step explanation:
Which number has the same absolute value
as 8
Answer:8
Step-by-step explanation:
Factorise fully
-14x - 8
ease do quick, will mark brainiest!
Answer:
-2( 7x+4)
Step-by-step explanation:
-14x - 8
Factor out -2
-2*7x -2*4
-2( 7x+4)
Answer:
2(-7x -4)Step-by-step explanation:
[tex] - 14x - 8[/tex]
Write -8 as -4×2
[tex] - 14x + 2 \times 4[/tex]
Factor out common term : 2
[tex]2( - 7x - 4)[/tex]
400 reduced by twice my age is 68 how old am i
hope it helps.........
Pls help - Solve for x
Answer:
-3
3x/(x^2+6x) = 1 is this the qstn?
if so then the ans is -3
Help Please! :(
108 students went on a field trip. Three buses were filled and 27 students traveled in cars. How many students were in each bus?
Please include algebraic equation and answer.
Answer:
81
Step-by-step explanation:
Find the equation of a line passing through the point (6,9) and (0,0)
Answer:
y=3/2x
Step-by-step explanation:
The equation of the required line as per slope-intercept form is 3x - 2y = 0.
What is the equation of a line passing through two points?The equation of a line that passes through points (x₁, y₁) and (x₂, y₂) is defined as:
m = (y₂ - y₁)/(x₂ - x₁)
Here, 'm' is the slope and 'c' is the y-intercept of the given line.
Therefore, the slope of a line that passes through (6, 9) and (0, 0) is
= (0 - 9)/(0 - 6)
= 3/2
Now, the general form of a line is y = mx + c. Here, 'm' is the slope and 'c' is the y-intercept of the line.
The line passes through the point (0, 0).
Therefore, 0 = (3/2) × 0 + c
⇒ c = 0
Now, the equation of the straight line is
y = (3/2)x + 0
⇒ 2y = 3x
⇒ 3x - 2y = 0
Learn more about equation of a line here: https://brainly.com/question/25283605
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