A musical instrument manufacturer hires you as consultants to help them sell their new trumpets.
through a customer survey, when the price of cach trumpet is $220.18, a total of 110 trumpets
would be sold at their la crosse store. the same survey said that if the price of each trumpet was
$160.74, a total of 128 trumpets would be sold. in order to make the new trumpet, the company
knows that it will have to buy (once and once only) $3274.78 of equipment, and after that, cach
individual trumpet will cost them $90.05 cach to make.
1) find the price-demand equation, assuming a linear model, with p for price and x for the number of trumpets
2) what should be the price of each trumpet to break even?
3) what should be the price of each trumpet to maximize profit?
Answers
1. The price-demand equation for the trumpets is:
x = 238.18 - 1.09p
2. The manufacturer should set the price of each trumpet at $296.50 to break even
3. The manufacturer should set the price of each trumpet at $138.63 to maximize profit.
In this problem, the manufacturer has conducted a customer survey and found out that the price of each trumpet affects the demand for it. We need to analyze this data and come up with a price-demand equation that helps the manufacturer set the price of each trumpet to maximize profit.
To start with, we need to assume a linear model, where the demand for the trumpets is directly proportional to the price. We can represent the demand as "x" and the price as "p". Using the data from the survey, we can form two linear equations:
110 = ap + b (1)
128 = cp + d (2)
Here, a, b, c, and d are constants that we need to find. We can solve these equations simultaneously to get the values of a, b, c, and d.
Subtracting equation (2) from equation (1), we get:
-18 = (a-c)p + (b-d) (3)
Dividing both sides of equation (3) by -18, we get:
p = (d-b)/(c-a) (4)
Using equation (4), we can find the value of p, which is the price at which the demand for trumpets is equal to the values obtained from the survey. Substituting the values from either equation (1) or (2) into equation (4), we get:
p = ($160.74 x 110 - $220.18 x 128)/(-18 x 110 + 18 x 128)
= $186.46
Therefore, the price-demand equation for the trumpets is:
x = 238.18 - 1.09p
To answer the second question, we need to find the price of each trumpet at which the manufacturer will break even. In other words, the revenue earned from selling the trumpets should be equal to the total cost incurred in making and selling them.
We know that the one-time cost of buying equipment is $3274.78, and each trumpet costs $90.05 to make. Let's represent the break-even price as "\(P_{be}\)". Then we can form the following equation:
110\(P_{be}\) = 3274.78 + 110 x 90.05
Solving for \(P_{be}\), we get:
\(P_{be}\)= $296.50
Therefore, the manufacturer should set the price of each trumpet at $296.50 to break even.
To answer the third question, we need to find the price of each trumpet that maximizes the profit for the manufacturer.
The profit is given by the revenue earned minus the total cost incurred. Let's represent the profit as "P" and the price as "p". Then the profit equation becomes:
P = xp - (3274.78 + 90.05x)
To find the price that maximizes profit, we need to take the derivative of the profit equation with respect to p and equate it to zero.
dP/dp = x - 90.05 = 0
Solving for x, we get:
x = 90.05
Substituting this value of x into the price-demand equation, we get:
p = $138.63
Therefore, the manufacturer should set the price of each trumpet at $138.63 to maximize profit.
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Related Questions
CAN SOMEONE PLS HELP ME FIND THE RANGE PLS PLS
Answers
Answer:
y is greater than or equal to 1
Step-by-step explanation:
The function opens upward and the lowest point is (2,1). The y-values are infinite as long as it is greater than 1.
Step-by-step explanation:
I guess D means domain, R means range.
and what is the question about Function ? if it is a function ? I assume that.
4)
the domain is the interval or set of all valid x (input) values.
there is nothing "forbidden" or strange in the expression, so, x can have any value from -infinity to +infinity.
-infinity < x < +infinity
5)
the range is the interval or set of all valid y (result) values.
if x = 0, y = -5
if x = 1, y = -8
if x = 2, y = -9
if x = 3, y = -8
if x = 4, y = -5
since such a parabola is a symmetric function, we see the vertex, the extreme point and point of symmetry to be x = 2.
and that is the minimum of the parabola (x = 2, y = -9), which is clearly opening up.
the range (of y) is therefore
-9 <= y < +infinity
or simply
y >= -9
6)
yes, it is a function, as every x has exactly one possible result value.
as we can see, multiple x values can have the same y value, but that is not a problem for a function. but one x value cannot have multiple y values (and that is clearly not violated here : every x has one y value).
Two pulleys, one with radius r 1r1 and the other with radius r 2r2, are connected by a belt. The pulley with radius r 1r1 rotates at omega 1ω1 revolutions per minute, whereas the pulley with radius r 2r2 rotates at omega 2ω2 revolutions per minute. Show that StartFraction r 1 Over r 2 EndFraction equals StartFraction omega 2 Over omega 1 EndFraction r1 r2
Answers
Answer:
r1/r2 = 2ω2/ω1
Step-by-step explanation:
The velocity of each pulley is expressed as v = ωr where;
v is the linear velocity of the pulley
ω is the angular velocity of the pulley
r is the radius of the pulley.
For the two pulleys, the velocity I'd both pulleys are the same.
v1 = v2
v1 is the linear velocity of first pulley
v2 is the linear velocity of the second pulley.
v1 = ω1r1
v2 = 2ω2(r2)
r1 and r2 is the radius of pulley 1 and pulley 2 respectively.
Since v1 = v2
ω1r1 = 2ω2(r2)
Divide both sides by r2
ω1r1/r2 = 2ω2(r2)/r2
ω1r1/r2 = 2ω2
Divide both sides by ω1
ω1r1/r2/ω1= 2ω2/ω1
r1/r2 = 2ω2/ω1
The function f(x) = 2x^3 – 36x^2 + 192x + 5 has one local minimum and one local maximum. This function has a local minimum at x equals with value and a local maximum at requals with value
Answers
The function has a local minimum at x = 8 with a value of 69, and a local maximum at x = 4 with a value of -267.
To find the local minimum and local maximum of the function f(x) = 2x^3 - 36x^2 + 192x + 5, we first need to find the critical points. We do this by finding the first derivative of the function and setting it equal to zero.
f'(x) = 6x^2 - 72x + 192
Now, set f'(x) = 0 and solve for x:
6x^2 - 72x + 192 = 0
Divide by 6:
x^2 - 12x + 32 = 0
Factor:
(x - 4)(x - 8) = 0
So, the critical points are x = 4 and x = 8. To determine whether these points are local minima or maxima, we can use the second derivative test.
Find the second derivative:
f''(x) = 12x - 72
Now, evaluate the second derivative at x = 4 and x = 8:
f''(4) = 12(4) - 72 = -24 (negative, so it's a local maximum)
f''(8) = 12(8) - 72 = 48 (positive, so it's a local minimum)
Finally, find the values of the function at these points:
f(4) = 2(4)^3 - 36(4)^2 + 192(4) + 5 = -267
f(8) = 2(8)^3 - 36(8)^2 + 192(8) + 5 = 69
So, the function has a local minimum at x = 8 with a value of 69, and a local maximum at x = 4 with a value of -267.
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How do you score 102 students play at least once by there is 40% of the students at the school how many students are at the school
Answers
If 102 students at least plays one sport and this is 40% of the students at the school, then there 255 students at the school
Let's assume that the total number of students in the school is "x".
40 percentage of the students at the school play at least one sport. So, the number of students who play at least one sport is 0.4x.
We also know that the number of students who play at least one sport is 102. Therefore, we can write:
0.4x = 102
Move 0.4 to the right hand side of the equation
x = 102 / 0.4
Divide the numbers
x = 255
Therefore, there are 255 students at the school.
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Blocking an experimental design is useful because
Answers
Answer:
it controls for multiple variables in an experiment.
Step-by-step explanation:
pls mark as brainliest
A research submarine dives at a speed of 100 ft/min directly toward the research lab. How
long will it take the submarine to reach the lab from the surface of the ocean?
It will take minutes for the submarine to reach the lab from the surface of the ocean
(Round to one decimal place as needed.)
Answers
Answer:29.2
Step-by-step explanation:
Answer:29.2m
Step-by-step explanation:
4 - dictado audio you will hear a conversation. Listen carefully and write what you hear during the pauses. The entire conversation will then be repeated so you can check your work
Answers
According to the conversation we can infer that the information focused on the conversation of two people; one of them is studing for an exam.
What is the conversation about?To identify what is the conversation about we have to consider who is talking and what are the ideas that they share. In this case, we can infer that the main idea of this conversation is that one of them is studying for an exam this week.
Also, the second person is apologizing because he considered that he is distracting the other person. So, the correc information about de conversation is a short conversation about study.
Note: This question is incomplete. Here is the complete information:
Conversation:
Hello
Hello, How are you?
I am fine, and you?
i am fine too, What are you doing?
I am studing for an exam this week.
Oh, sorry I won´t distract you.
Don´t worry.
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The Chan’s minivan requires 5 gallons of gasoline to travel 120 miles. How many gallons of gasoline will they need to travel 360 miles?
Answers
Answer:
15 gallons
Step-by-step explanation:
360 divided by 120= 3
3×5=15
helppp please i dont know how to do this
Answers
The solution of the pairs of lines are as follows,
(1) Line 1 and line 2 are perpendicular to each other.
(2) Line 1 and line 3 are parallel to each other.
(3) Line 2 and line 3 are perpendicular to each other.
The slope of the line is a tangent angle made by line with horizontal. i.e. m =tanx where x in degrees.
Here,
Calculate the slope of each line,
LIne 1
3y = 2x + 5
y = 2/3x + 5/3
Compared with the standard equation of line y = mx + c,
Slope m = 2/3
Similarly.
The slope of line 2 = -3/2
The slope of line 3 = 2/3
Now. properties of pair of lines state that the slope of parallel lines is equal and the slope of perpendicular lines are negative reciprocal of each other,
So
Slope of line 1 = slope of line 3
But,
The slope of line 2 is the negative reciprocal of the slope of lines 1 and 3.
Thus, the solution of the pair of lines has been shown above.
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Which graph best represents the download speed of a large file?
P.S. I will give brainliest to the best answer!
Answers
Answer:
graph d because it starst out slower and then ends off faster
The graph that correctly represents the given case is B.
What is the slope of straight line?The slope of a straight line is the tangent of the angle formed by it with the positive x axis as the reference.
The negative slope indicates the rate of decrease while the positive shows the rate of increase.
All the graphs are examined one by one as follows,
(A) In the graph A, The slope is negative.
Which implies the the speed will slow down.
(B) In the graph B, The slope is positive.
Which implies the the speed will rise up.
(C) ) In the graph C, The slope is zero.
Which implies the the speed will be constant.
(D) In the graph D, The slope is positive and it has a y intercept.
Which implies the the speed will rise from a non zero value.
Thus, in order to download a large file the suitable graph is (B).
Hence, the given case can be represented by graph B.
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Ben earns $13 per hour at Starbucks. When he works overtime, he earns time and a half. What is his regular pay for 40 hours of work?
Answers
Answer:
$520
Step-by-step explanation:
Ben earns $13 per hour of regular work
He gets for 40 hours of regular work:
$13*40 = $520Answer is $520
Overtime is (time+half) = $13 + $13/2 = $13 + $6.5 = $19.5
So, his regular pay (40 h/week) would be = $2,253.67
Whoever has the correct answer gets brainliest! What is the area of this trapezoid? This is Geometry by the way.
Answers
Answer:94.5
Step-by-step explanation:
Questions 5)
Scientists estimate that a single atom is 10
-10
meters
across, while a proton is 10-15
meters across. Which
is larger and how much larger is it?
A) Atom
B) Proton
Answers
Answer:
the answer is for the question you are asking is A) Atom
Find an equivalent ratio in simplest terms: 70:40
Answers
Answer:
7:4
Step-by-step explanation:
70 / 2 : 40 / 2
35:20
35 / 5 : 20 / 5
7:4
The length of the highway is 600 miles. If 2 inches represent 75 miles, what is the length of the highway on the map?
Answers
Answer:
16 inches
Step-by-step explanation:
The variables in this equation are miles and inches. You're given the ration 2 inches: 75 miles. Take the other factor that you are given, which for this problem would be 600 miles, and divide it by the number with the same variable, which would be 75 miles. This comes out to be 8, to which you then multiply that by the number with the variable that you are trying to find, which is two. Therefore, the length of the highway on the map would be 16 inches.
In 2015, around ____ percent of the world’s population had an internet connections.
Answers
The sum of two consecutive
whole numbers is 57. Write and
solve an equation to find the
numbers
Answers
Answer:
28 , 29
Step-by-step explanation:
Let the two consecutive numbers be x and x + 1
x + x + 1 = 57
Combine like terms
2x + 1 = 57
Subtract 1 from both sides
2x = 57- 1
2x = 56
Divide both sides by 2
x = 56/2
x = 28
x + 1 = 28 + 1 = 29
the curve x = t2 − 3t, y = t intersects the y-axis when x = 0, which occurs when t = 0 and
Answers
The curve x = t^2 − 3t, y = t intersects the y-axis when x = 0, which occurs when t = 0 and t=3. is 8root2/5
What does intersect mean in math?When two or more lines cross each other in a plane, they are called intersecting lines. The intersecting lines share a common point, which exists on all the intersecting lines, and is called the point of intersection. Here, lines P and Q intersect at point O, which is the point of intersection.
What is the intersection of a curve?In general, an intersection curve consists of the common points of two transversally intersecting surfaces, meaning that at any common point the surface normals are not parallel. This restriction excludes cases where the surfaces are touching or have surface parts in common.
A=∫ ( t)(2t−2)dt
=∫ 2t ^(3/2) −2t ^(1/2)dt
=8root(2)/15
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The length of a rectangle is 3 inches longer than it is wide. If the area is 108 square inches, what are the dimensions of the rectangle
Answers
Answer:
width = 9 inches , length = 12 inches
Step-by-step explanation:
let width be w then length = w + 3
area (A) of a rectangle is calculated as
A = length × width
= (w + 3) × w = w(w + 3) = w² + 3w
given A = 108 , then
w² + 3w = 108 ( subtract 108 from both sides )
w² + 3w - 108 = 0 ← in standard form
(w + 12)(w - 9) = 0 ← in factored form
equate each factor to zero and solve for w
w + 12 = 0 ⇒ w = - 12
w - 9 = 0 ⇒ w = 9
however, w > 0 , so w = 9 and w + 3 = 9 + 3 = 12
then width = 9 inches and length = 12 inches
9-7w=8w+8
what is w??
Answers
Answer:
w=1/15
Step-by-step explanation:
Step 1: Simplify both sides of the equation.
9−7w=8w+8
9+−7w=8w+8
−7w+9=8w+8
Step 2: Subtract 8w from both sides.
−7w+9−8w=8w+8−8w
−15w+9=8
Step 3: Subtract 9 from both sides.
−15w+9−9=8−9
−15w=−1
Step 4: Divide both sides by -15.
−15w/−15 = −1/−15
w = 1/15
-15w=-1
w=-1/-15
w=0.6666.......
n - 5 = 3n + 1
solve for n.
Answers
Answer:
-3
Step-by-step explanation:
n-5=3n+1
3n-n= -5-1
2n= - 6
n=-3
WILL GIVE BRAINLIEST PLEASE HELP
Ryan and Eduardo are saving up money for a vacation to Italy. They have calculated that the trip will cost at least $900. If they’ve already saved $270, how much more do they need to save in order to have enough for the trip? Write an inequality and solution set
Answers
Answer:
they need to save $630 in order to have enough for the trip
270 + 630 = $900
Solve equation and show all steps what is 3/8x=36
Answers
Answer:
x=96
Step-by-step explanation:
3/8x=36
Multiply both sides by 8/3.
\((\frac{8}{3}) (\frac{3}{8} x)=(\frac{8}{3} )\)
x =96
Answer:
96
Step-by-step explanation:
36/3/8=36*8/3.
Therefore, 36*8 is 288,
Then you divide 3 from 288=288/3=96
The answer is 96.
Hopefully this answer helps!!!
What is -5 5/8 + 3 1/2? Answer now for 25 points and a brainly!
-3 1/8
-2 1/2
-2 1/8
- 7/8
Answers
==============================================
Work Shown:
5 & 5/8 = 5 + 5/8
-5 & 5/8 = -(5 & 5/8) = -(5 + 5/8) = -5 - 5/8
So,
( -5 & 5/8 ) + ( 3 & 1/2 )
( -5 - 5/8 ) + ( 3 + 4/8 )
( -5+3 ) + ( -5/8+4/8 )
-2 + (-1/8)
-(2 + 1/8)
-(2 & 1/8)
-2 & 1/8
------------------------
Alternative Method
We could convert each mixed number to decimal form
-5 & 5/8 = -5-5/8 = -5.625
3 & 1/2 = 3+1/2 = 3.5
( -5 & 5/8 ) + ( 3 & 1/2 ) = -5.625+3.5 = -2.125
Then convert back to mixed number form
-2.125 = -2 & 125/1000
-2.125 = -2 & (1*125)/(8*125)
-2.125 = -2 & 1/8
Answer:C is you answer
Step-by-step explanation:
Gravity Versus Distance
What is the force of gravity on the rocket at the planet's surface?
What is the force of gravity on the rocket at a distance of two units (twice the planet's radius from its center)?
According to the graph, is the relationship between gravity and distance linear or nonlinear? Explain.
In general, how does the force of gravity pulling on the rocket change as the distance between it and the planet increases?
Estimate the force of gravity on the rocket at a distance of 5 units.
Answers
Answer:
How many feet are there in 150 centimeters? *
What is the area of the figure she created?
Answers
Answer:
27 FT
Step-by-step explanation:
Area of square = L × W
= 4.5 ft × 4.5 ft
= 20.25 ft
Area of parallelogram = bh (base times height)
= 1.5 ft × 4.5 ft
= 6.75 ft
Total area = 20.25 ft + 6.75 ft
= 27 ft
HOPE THIS HELPED
What is the solution set of the quadratic inequality 6x² + 1 ≤0?
O {X[XER}
O
{X1 X=-1}
Answers
Answer:
The empty set
Step-by-step explanation:
The square of a real number is non-negative, and thus the left hand side is always positive.
Please solve this is a not a test or quiz it is a question by my teacher as how to solve the problem
Answers
Answer:
0
Explanation:
Consider the diagram below:
Point P divides segment CD in the ratio 3:2.
To find the coordinate of P, we use the formula for the internal division of a line segment given below:
\(P(x,y)=\mleft(\dfrac{mx_2+nx_1}{m+n},\dfrac{my_2+ny_1}{m+n}\mright)\)Thus, the x-coordinate of P is:
\(\begin{gathered} \dfrac{mx_2+nx_1}{m+n}=\frac{3(4)+2(-6)}{3+2}\text{ where }\begin{cases}m\colon n=3\colon2 \\ x_1=-6,x_2=4\end{cases} \\ =\frac{12-12}{5} \\ =\frac{0}{5} \\ =0 \end{gathered}\)The x-coordinate of P is 0.
Extra
The y-coordinate of P is:
\(\begin{gathered} \dfrac{my_2_{}+ny_1}{m+n}=\frac{3(5)+2(0)}{3+2}\text{ where }\begin{cases}m\colon n=3\colon2 \\ y_1=0,y_2=5\end{cases} \\ =\frac{15+0}{5} \\ =\frac{15}{5} \\ =3 \end{gathered}\)The y-coordinate of P is 3.
What is the HCF of 18,54 and 81
Answers
Answer:9
Step-by-step explanation:
I got 60p and 70p but that doesn't work, so i need help pls. again, pretty simple question but mt brain isn't working
Answers
Step-by-step explanation:
let's reffer to:
gumbo (x)
raspberry (y) so,
8x + 9y =14. 3 (1)
6x + 3y = 8.1 (2)
devide (2) by 3
2x + y = 2.7
y = 2.7 - 2x (3)
substitute 3 in 1
8x + 9(2.7 - 2x) = 14.3
8x + 24.3 - 18x = 14.3
10 x = 10
x = 1 (ANS)
and y = 0.7 (ANS)
Answer:
Hello There the correct answer to this is The first one is 1029.6 Because you need to multiply 8 x 9 then it will be 72 and then multiply 72 x 14.30 it will be 1029.6 it will the same the Second one is 145.8 Because you you need to multiply the first one multiply 6 x 3 which that 18 the multiply 18 x 8.10 which that will be 145.8 SO both of these answer are the same.
Hope It Helps!
ItsNobody