A company estimates that it can sell 3,000 units each month of its product if it prices each unit at $80. However, its monthly number of sales will increase by 10 units for each $0.10 decrease in price. The company has fixed costs of $250. The cost to make each unit is $4.20. Find the level of production that maximizes the company's profit.
The Should Produce _________
Units at a price of $__________
Which will yield a profit of $_______
9514 1404 393
Answer:
5290 units$57.10 per unit$279,591 profitStep-by-step explanation:
For price p, the quantity q of units sold is said to be ...
q = 3000 +10(80-p)/0.10 . . . . for price in dollars
Then the revenue will be ...
r(p) = p·q = p(3000 +100(80-p)) = 100p(110 -p)
The cost is said to be ...
c(q) = 250 +4.20q
c(p) = 250 +4.20(100(110 -p)) = 250 +420(110 -p)
Then the profit function is ...
P(p) = r(p) -c(p)
P(p) = 100p(110 -p) -(250 +420(110 -p)) = (110 -p)(100p -420) -250
__
Ignoring the vertical offset of -250, the quadratic has zeros at 110 and 4.2. So, its line of symmetry (and vertex) will be found at ...
p = (110 +4.2)/2 = 57.1 . . . . dollars per unit
The quantity that should be produced at that price is ...
q(57.1) = 100(110 -57.1) = 5290 . . . . units produced
The profit at that price is ...
P(57.1) = (110 -57.1)(100·57.1 -420) -250 = 52.9(5290) -250
= $279,591 . . . . best profit
_____
Additional comment
After you have seen a few of these, you can write down the revenue function based on the rate of change of units sold.
If p is the price of a unit, then 80-p is the number of dollars of decrease in price for a price of p. Then (80 -p)/0.10 is the number of 10¢ decreases in price. The increase in units sold is 10 times this, or 10(80 -p)/0.10 = 100(80 -p). When that is added to 3000 units sold, the total is ...
3000 +100(80 -p) = 3000 +8000 -100p
= 11000 -100p = 100(110 -p) . . . . . quantity sold at price p
Revenue is the product of price times the number of units sold at that price.
Profit is the difference between revenue and cost.
The function f(x) = −(x + 5)(x + 1) is shown. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 3, 4), and goes through (negative 1, 0). What is the range of the function? all real numbers less than or equal to 4 all real numbers less than or equal to −3 all real numbers greater than or equal to 4 all real numbers greater than or equal to −3 Mark this and return
Answer:
All real numbers less than or equal to 4.
f(x) ≤ 4
Interval notation: (-∞, 4]
Step-by-step explanation:
Given the quadratic function, f(x) = -(x + 5)(x + 1), where the vertex occurs at point, (-3, 4):
Since the graph of the parabola opens down, then it means that the vertex is its maximum point. In reference to the vertical points on the graph (i.e., the range values), then the vertex sets the maximum range value of k = 4. This implies that the maximum possible range value is from negative infinity to positive 4.
Therefore, the range of the function is: all real numbers less than to or equal to 4.
f(x) ≤ 4
Interval notation: (- ∞, 4]
Answer:
its A on edge
Step-by-step explanation:
Just took the test
Which relationships describe angles 1 and 2? Select each correct answer.
Adjacent angles
Vertical angles
Complementary angles
Supplementary angles
Answer:
They are adjacent angles and supplementary angles.
Step-by-step explanation:
∠1 and ∠2 are supplementary angles because they form a linear pair who sum = 180°
∠1 and ∠2 are adjacent angle because they are next to each other or you can say that they share a common side and have the same vertex.
Please help shakdnjdissnbxjddbbd
Answer:
Step-by-step explanation:
# Store uploaded files on the local file system in a temporary directory.
config.active_storage.service = :test
The website
Constructed Response
Two skyscrapers are under construction in Atlanta. They will sit on opposite sides of Peachtree St. and
the architect has designed them to be similar. The architect made a sketch of two rectangles to model
the front view of the two buildings and included the following statement: ABCD ~ JKLM. It was also given
that AB = 1600 ft., BC = 200 ft., and JM = 150 ft.. Use the scenario to solve problems (a) through (d)
a.) Which rectangle is being used to model the taller building?
b.) Which line segments could be used to model the height of the smaller building?
c.) What is the height of the taller building? Explain your reasoning.
d.) What is the height of the smaller building? Explain your reasoning.
e.) Would it make sense to say that the scale factor from smaller building to taller building is 3/4?
Explain your reasoning.
A rectangle is a quadrilateral which has the length of its opposite sides to be equal. Thus, the following are the solutions to the questions:
a) The rectangle used to model the taller building is ABCD.
b) The line segment used to model the height of the smaller building is JM = KL.
c) The height of the taller building is 200 feet.
d) The height of the smaller building is 150 feet.
e) Yes, the scale factor from small to tall building is [tex]\frac{3}{4}[/tex].
Rectangles have equal length of opposite sides , and the sum of its interior angles to be [tex]360^{o}[/tex]. Since the two given skyscrapers were modeled with respect to rectangles ABCD and JKLM, then the answers to the questions are:
a) The rectangle used to model the taller building is ABCD. Since the length of a rectangle is always greater than its width. So that the height; AD = BC.
b) The line segment that can be used to model the height of the smaller building is; JM = KL. This represent the width of the rectangular model for the small building.
c) The height of the taller building is AD = BC = 200 feet. The width of a rectangle is often smaller than its length, which in this case is the height.
d) The height of the smaller building is JM = KL = 150 feet. The length of a rectangle is usually longer than its width.
e) Yes, it would make sense because:
scale factor = [tex]\frac{height of the smaller building}{height of the taller building}[/tex]
= [tex]\frac{150 ft}{200ft}[/tex]
= [tex]\frac{15}{20}[/tex]
scale factor = [tex]\frac{3}{4}[/tex]
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Tyreese is using algebra tiles to solve the equation below.
2 x + 5 = negative x + (negative 1)
Tyreese’s first step is to
remove one x-tile from both sides.
remove two x-tiles from the left side.
add one positive x-tile to both sides.
add two positive x-tiles to both sides.
[tex]2x + 5 = - x + ( - 1)[/tex]
[tex]2x + 5 = - x - 1[/tex]
Add both sides x
[tex]2x + 5 + x = - x - 1 + x[/tex]
[tex]3x + 5 = - 1[/tex]
Subtract both sides 5
[tex]3x + 5 - 5 = - 1 - 5[/tex]
[tex]3x = - 6[/tex]
Divide both sides by 3
[tex] \frac{3x}{3} = \frac{ - 6}{3} \\ [/tex]
[tex]x = - 2[/tex]
______________________________
As u can see the first step is to :
Add one positive x-tile to both sides
Answer:
Add one positive x-tile to both sides
Step-by-step explanation:
edge
Ax + 4 = 6x + B
What values of A and B will result in an equation with infinite solutions? Enter the answers in the boxes.
A=
B=
Answer:
A = 6 + B /x − 4 /x
B = Ax + 4 − 6 x
x = b-4/a-6
Step-by-step explanation:
hope this helps :)
The values of A and B that will result in an equation with infinite solutions are 6 and 4
Infinite solution of an equationFor an equation to have infinite number of solutions, the equations on both sides must be the same,
Given the equation
Ax + 4 = 6x + B
If the equation has infinite number of solution, then
Ax = 6x
A= 6
Similarly
4 = B
B = 4
Hence the values of A and B that will result in an equation with infinite solutions are 6 and 4
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what is this? 30 points!!!!
Answer: X = -351
Step-by-step explanation:
Answer:
x=117
Step-by-step explanation:
Let A = { 1, 2, 5, 7 } and B = { 1, 5, 9, 12 }. Write each of the following sets.
1. A ∩ b
2. A ∪ B
Answer:
1,5 answer of 1 St questions
1,2,5,7,9,12 answer 2nd questions
Step-by-step explanation:
1.A ∩ B
A { 1, 2, 5, 7 } and B = { 1, 5, 9, 12 }.
They have both five and one so the answer is
A ∩ B= {1,5}
2. A ∪ B
You only need to list everything(but no repetition) so the answer is
{ 1, 2, 5, 7, 9, 12 }
Find the equation of this line plz help
Answer:
y = - [tex]\frac{1}{2}[/tex] x + 1
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (0, 1) and (x₂, y₂ ) = (4, - 1) ← 2 points on the line
m = [tex]\frac{-1-1}{4-0}[/tex] = [tex]\frac{-2}{4}[/tex] = - [tex]\frac{1}{2}[/tex]
The line crosses the y- axis at (0, 1 ) ⇒ c = 1
y = - [tex]\frac{1}{2}[/tex] x + 1 ← equation of line
What is the value of t?
Answer:
53°
Step-by-step explanation:
83 + 44 + x = 180
=> 127 + x = 180
=> x = 180 - 127
=> x = 53°
Hoped this helped.
Please help me
Here it is
I will mark you brainliest if you help with all of these
Answer:
1. 3/2
2. 1
3. -5/3
4. 5/4
5. -5/9
6. 4/5
7. 8/5
8. 1/4
9. 1/2
10. 2/3
11. 0
12. -1/3
13. 1
14. -1
Step-by-step explanation:
Jeremiah and Tristan work at a dry cleaners ironing shirts. Jeremiah can iron 35 shirts per hour, and Tristan can iron 20 shirts per hour. Jeremiah and Tristan worked a combined 17 hours and ironed 490 shirts. Determine the number of hours Jeremiah worked and the number of hours Tristan worked.
The length of a rectangle is 5 inches more that the width. The perimeter is 46 inches. Find the length and the width.
Answer:
1. Use variables to represent length and width.
width = w
length = w + 5
2. Set up an equation for the perimeter of the rectangle.
perimeter = 2L + 2W
2(w + 5) + 2(w) = 46
2w + 10 + 2w = 46
4w + 10 = 46
4w = 36
w = 9
3. Find the length and width of the rectangle.
width = w = 9 inches
length = w + 5 = 14 inches
Answer:
Width is 9 inches
Length is 14 inches
Step-by-step explanation:
width = w
length = w + 5
perimeter = 2L + 2W
2(w + 5) + 2(w) = 46
2w + 10 + 2w = 46
4w + 10 = 46
4w = 36
w = 9
Width = w = 9 inches
Length = w + 5 = 14 inches
Therefore the width is equal to 9 inches and the length is 14 inches.
(The quotient of a number and the sum of the number and eight) Help to translate this for me thank you!!!!
Answer:
(1+8)
Step-by-step explanation:
(+8)
I need the answer please asp
Answer:
The answer is a isosceles right I think.
MATH QUESTION HELP ASAP!
Answer:
-9/10
Step-by-step explanation:
Yw, me!
A football team charges $30 per ticket and averages 20,000 people per game. Each person spend an average of $8 on concessions.For everydrop of $1 in price,the attendance rises by 800 people.What ticket price should the team charge to maximize total revenue? Calculate the TR max.
The price that would maximize total revenue would be $ 23.
As long as that a football team charges $ 30 per ticket and averages 20,000 people per game, and each person spend an average of $ 8 on concessions, and for every drop of $ 1 in price, the attendance rises by 800 people, to determine what ticket price should the team charge to maximize total revenue, the following calculation must be performed:
20,000 x 30 + 20,000 x 8 = 760,000 24,000 x 25 + 24,000 x 8 = 792,00024,800 x 24 + 24,600 x 8 = 792,00025,600 x 23 + 25,600 x 8 = 793,600 26,400 x 22 + 26,400 x 8 = 792,000
Therefore, the ticket price that would maximize the total revenue would be $ 23.
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PLEASE HELP
(delta math)
Triangle IJK is formed by connecting the midpoints of the side of triangle FGH.
The lengths of the sides of triangle IJK are shown. What is the length of FH?
Figures not necessarily drawn to scale.
H
5
5
hi me ////// ///////////
20. The number of babies out of 1,000 that die during their first year of life is called:
A. infant morbidity rate
B. infant mortality rate
C. fertility rate
D. death rate
The answer is B
the explanation is not needed
Answer:
B
Step-by-step explanation:
the amswer will be infant mortality rate
Question 5 of 10
The graph shows the function f(x) = 2^x.
What is the value of x when f(x) = 4?
Answer:
A. 2
Step-by-step explanation:
Our y-axis is equivalent to f(x), so we can use it to find the value of x when f(x) = 4. If we look at the graph, we can find that an f(x) value of 4 (or, a y-value of 4) has an x-value of 2.
We could also figure this out by making f(x) equal to 4 in the equation:
[tex]4=2^{x}[/tex]
2 times itself how many times is equal to 4? Well, 2 times 2 is equal to 4, so 2 times itself two times is equal to 4. x is equal to 2:
[tex]4=2^{2}[/tex]
Either way works. If you have any more questions, let me know! :)
What is the y-intercept of
y = 4x – 12?
A) 4
B)-4
C)-12
D) -3
Answer:
C, -12
Step-by-step explanation:
If y = mx + b
then m = 4
and b = -12
b is the y-intercept
this can be plotted on a graph as {0, -12}
Hope this helps
I need some help solving this equation T^T
5x(-y)+2=-3
Answer:
first subtract the 2 cancelling out on the left side, making the -3 a -5, then add y cancelling out the left side, making the right side -5+y, than your equation is 5x=-5+y, dividing the 5 off makes x=-5+y/5. :)
Suppose you obtain a $4,000 T-note with a 4% annual rate, paid half-yearly, with maturity in 5 years. How much (simple) interest will you earn?
3) I get a 15% employee discount, but then have to pay 8.2% tax on the discounted price. What do I pay for a $300
item?
Answer:
$243.45
Step-by-step explanation:
300 * 0.15 = 45
300 - 45 = $225
$225 is the discounted price
225 * 0.082 = 18.45
225 + 18.45 = $243.45
You would pay $243.45 for the item.
Ron has five books on chemistry. He wants to mail the books. He weighs the books. Which unit should he use to measure the weight of books?
Answer:
Pounds
Step-by-step explanation:
Grams is used for smaller objects, and liters is used for a liquid, centimeters, is used to measure distance, and same with yards,feet,kilometers, meters. the correct answer is pounds.
Ron weighs the books so he uses to pound unit to measure the weight of the books.
What are units of measurement?The group of units used to quantify different physical quantities is collectively known as the units of measurement. Since ancient times, we have measured these things using many units, including length, mass, volume, current, and temperature. Since then, these units of measurement have changed, and we now use new, more practical and user-friendly systems of measurement.
Centimetres are used to measure distance, same as yards, feet, kilometres, and metres are used to measure larger objects, liquids are measured in litres, and tiny objects are measured in grammes.
Since Ron weighs the books so he uses to pound unit to measure the weight of the books.
Therefore, the correct answer would be pound.
Hence, he weighs the books so he uses to pound unit to measure the weight of the books.
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PLEASE HELP ME PLEASE IM DESPERATE ILL MARK BRAINLIEST
Answer:36in
Step-by-step explanation:
Answer: 36in
Step-by-step explanation: Its 36in because if you add them all up then you get 36. (hope it helps +)
can someone help me plzzz!!
Answer:
x = 2 and y = -2
Step-by-step explanation:
a) 5x-4y = 18
b) x+3y = -4
b) x = -3y - 4
a) 5 (-3y - 4) - 4y = 18 (substitution)
a) - 15y - 20 - 4y = 18
a) -19y = 18 + 20
a) y = 38/-19
y = -2
b) x + 3(-2) = -4
b) x - 6 = -4
x = 6-4 = 2
Calculate 2 2/5 - 1 2/3
Answer:
25 4 12334
Step-by-step explanation:
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