The marketing department at XYZ Company has found that, when Product ABC is sold at a price of p dollars per unit, the number x of Product ABC sold is given by the demand equation = 280 – 14p. - (a) Find the model that expresses the revenue R as a function of the price p. (Note that R хр, the unit price times the number of units sold) R(p) (b) Explain how would you find the price that will maximize the revenue (the optimal price), and the maximum revenue. Use the box below to type your answer. Edit - Insert Formats В I U x, x² A (c) Find the optimal price and the maximum revenue. The optimal price: dollars The maximimum revenue: dollars

The marketing department at XYZ Company has found that, when Product ABC is sold at a price of p dollars per unit, the number x of Product ABC sold is given by the demand equation = 280 – 14p. - (a) Find the model that expresses the revenue R as a function of the price p. (Note that R хр, the unit price times the number of units sold) R(p) (b) Explain how would you find the price that will maximize the revenue (the optimal price), and the maximum revenue. Use the box below to type your answer. Edit - Insert Formats В I U x, x² A (c) Find the optimal price and the maximum revenue. The optimal price: dollars The maximimum revenue: dollars

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: 2. When a patient is given a vitamin B-12 treatment to promote red blood cell formation, the dose D,…

A: Need to find dosage for weighing 175 pounds

Q: Find the y- intercept of a straight line passing through the point(2,4) whose gradient is 3.

A: Given that The point x1,y1=2,4 The gradient m =3

Q: how do you find the slope when given a table of x and y's?

A: To determin the slope from table of x and y.

Q: Prove that if f(x) > 0, lim f(x) = 0, and 6. х а lim g(x) = ∞, then lim f(x)s(x) = 0. х а ха

A: To prove: Formula used:

Q: One action that a government could take to reduce carbon emission into the atmosphere is to place a…

A: One action that a government could take to reduce carbon emission into the atmosphere is to place a…

Q: Write down the gradient of the straight line represented by the equation y = −0.05t + 47. What does…

Q: 9. y = 3x2 – 2vx at (1, -9)

A: To find slope.

Q: What is the slope for the function y = 2x2 + 2 at the point x 3?

A: given y=2x^2+2

Q: The number of fat grams f consumed daily by the average American can be approximated by f 165 +…

Q: Determine the equation of the line tagent to the function f(x)=x(5-x)4 at x=3

Q: A coffee shop currently sells 470 lattes a day at $3.50 each. They recently tried raising the by…

Q: Find three solutions for this function: X-4 f(x) = %3D 2х-8 O (( x, y):(1, – X0, 1)(1, –)} O ((x,…

A: The given function is:fx=x-42x-8

Q: A certain mountain has an elevation of 19,273 feet. In 1921, the glacier on this peak covered 4…

A: A certain mountain has an elevation of 19,273 feet. In 1921, the glacier on this peak covered 4…

Q: .3 The curve y = ax + bx? + cx + 5 touches the x -axis at P(-2,0)and cuts the y-axis at the point Q…

Q: 22. Given the function f(x) = -2x²-16x-29, a) find the slope of the line tangent to the function at…

Q: 1. Recent studies indicate that the average surface temperature of the earth has been rising…

A: According to Bartleby guidelines we are supposed to do the first one of multiple questions Kindly…

Q: Let f(x)= ex and g(x) = 2x. For all x-values, f(x) > g(x). True False

Q: 8. The Federal debt held by the public as a percent of the gross domestic product (GDP) is modeled…

A: Solution

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

The marketing department at XYZ Company has found that, when Product ABC is sold at a price of p
dollars per unit, the number x of Product ABC sold is given by the demand equation
= 280 – 14p.
-
(a) Find the model that expresses the revenue R as a function of the price p. (Note that R
хр, the
unit price times the number of units sold)
R(p)
(b) Explain how would you find the price that will maximize the revenue (the optimal price), and the
maximum revenue. Use the box below to type your answer.
Edit -
Insert
Formats
В
I U x, x²
A
(c) Find the optimal price and the maximum revenue.
The optimal price:
dollars
The maximimum revenue:
dollars

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Given information

VIEW

Step 2: Revenue maximization

VIEW

Step 3: Final answer

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Find the equation of line (L) that passes through the intersection point of the two functions y = v2 - x and y- 2x + 3 = 0 and perpendicular to the QI line 2x - 4y = 6
Determine the equation of the curve whose slope at any point is equal to through the point (-1,2)? y² - 2xy = 8 3x² + 2xy = -1 OD y = x lnx-2x x² - 4y² = -15 O A and which passes OB
The U.S. population can be modeled by the function y=165.6x¹.345, where y is in thousands and x is the number of years after 1800. (a) What was the population in 1970, according to this model? (b) is the graph of this function concave up or concave down? What does this mean? (c) Use numerical or graphical methods to find when the model estimates the population was 94,150,000. (a) According to the model, the population in 1970 was thousands. (Round to the nearest integer as needed.)
1) Consider a function that relates tax revenues R (in billions of dollars) to the average tax rate (t) such that R = 700t – 1000t2a. What average tax rate(s) is consistent with raising tax revenues equal to $120 billion?b. What average tax rate(s) is consistent with raising tax revenues equal to $122.5 billion?
find the gradient of the line (BC) passing through the point B (-3,8) and C (1,-12)
Find the value of y between the points (2, y) and (5, − 1) with slope − 3.
Solve for the slope of each of the given point of a function
Suppose that z is a linear function of and y with slope 3 in the direction and slope 2 in the y direction. (a) A change of -0.3 in x and -0.3 in y produces what change in z? change in z = (b) If z = 4 when x = 6 and y = 7, what is the value of z when x = 6 and y = 7.1? 2 =
"A company makes logo t-shirts for music festivals. Their total cost function is linear, and the total cost of making 60 t-shirts is $4281, whereas the total cost for 280 t-shirts is $7581. Assume a represents the number of t-shirts made. (a) Find the slope of the total cost function, C(x). slope = (b) Write the equation for the total cost function, C'(x). C(x) = 250
Sarah pays a flat rate plus a rate per minute for her phone plan as shown in the graph above. The cost of Sarah's phone plan, C(t), can be represented by which of the following functions? A: C(t) = -0.10t+25 B: C(t) = 0.10t+25 C: C(t) = 25(0.10)^t D: C(t) = 25(1+0.10)^t
10. The number of male alates in an ant colony has been found to be approximately a linear function of the age of the colony, with a 5-year-old colony having 8.2 alates on average, and a 17-year-old colony having an average of 33.4 alates. Write the number of male alates ( y ) as a linear function of the age of the colony in years (t).