Homework Help is Here – Start Your Trial Now!
Math
Calculus
The Physics Club at Foothill College sells Physics Show sweatshirts at the yearly Physics Show event. A quadratic regression model based on previous sales reveals the following demand equation for the sweatshirts: q = -p² +33p+9; 18≤p ≤28 A) Determine the price elasticity of demand E when the price is set at $20. SHOW WORK. B) Is demand elastic or inelastic at a price of $20? What will happen to revenue if we raise prices? Explain. C) At what price should sweatshirts be sold to maximize revenue? SHOW WORK. D) How many sweatshirts would be demanded if they were sold at the price that maximizes weekly revenue? SHOW WORK. E) What is the maximum revenue? SHOW WORK.

The Physics Club at Foothill College sells Physics Show sweatshirts at the yearly Physics Show event. A quadratic regression model based on previous sales reveals the following demand equation for the sweatshirts: q = -p² +33p+9; 18≤p ≤28 A) Determine the price elasticity of demand E when the price is set at $20. SHOW WORK. B) Is demand elastic or inelastic at a price of $20? What will happen to revenue if we raise prices? Explain. C) At what price should sweatshirts be sold to maximize revenue? SHOW WORK. D) How many sweatshirts would be demanded if they were sold at the price that maximizes weekly revenue? SHOW WORK. E) What is the maximum revenue? SHOW WORK.

Calculus: Early Transcendentals
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
icon
Related questions
Question

Show all work, thanks.

### Physics Club Sweatshirt Sales Analysis The Physics Club at Foothill College sells Physics Show sweatshirts at the yearly Physics Show event. A quadratic regression model based on previous sales reveals the following demand equation for the sweatshirts: \[ q = -p^2 + 33p + 9 \] \[ 18 \leq p \leq 28 \] Where: - \( q \) is the quantity of sweatshirts demanded - \( p \) is the price of the sweatshirts Analyzing this model involves answering the following questions: #### A) Determine the Price Elasticity of Demand (E) when the Price is set at $20. SHOW WORK. To determine the price elasticity of demand (E), we use the formula: \[ E = \left(\frac{dQ}{dp}\right)\left(\frac{p}{Q}\right) \] 1. Calculate \( \frac{dQ}{dp} \): \[ q = -p^2 + 33p + 9 \] \[ \frac{dq}{dp} = -2p + 33 \] 2. Substitute \( p = 20 \) into \( q \): \[ q = -(20)^2 + 33(20) + 9 \] \[ q = -400 + 660 + 9 \] \[ q = 269 \] 3. Substitute \( p = 20 \) into \( \frac{dq}{dp} \): \[ \frac{dq}{dp} = -2(20) + 33 \] \[ \frac{dq}{dp} = -40 + 33 \] \[ \frac{dq}{dp} = -7 \] 4. Calculate E: \[ E = \left(\frac{dQ}{dp}\right)\left(\frac{p}{Q}\right) \] \[ E = (-7)\left(\frac{20}{269}\right) \] \[ E \approx -0.52 \] #### B) Is demand elastic or inelastic at a price of $20? What will happen to revenue if we raise prices? Explain. Given \( |E| \approx 0.52 \) (which is less than 1), the demand is inelastic. **Explanation:** - If the price increases, the percentage decrease in quantity demanded will be smaller than the percentage increase in price. - Hence, raising prices will increase total revenue
Transcribed Image Text:### Physics Club Sweatshirt Sales Analysis The Physics Club at Foothill College sells Physics Show sweatshirts at the yearly Physics Show event. A quadratic regression model based on previous sales reveals the following demand equation for the sweatshirts: \[ q = -p^2 + 33p + 9 \] \[ 18 \leq p \leq 28 \] Where: - \( q \) is the quantity of sweatshirts demanded - \( p \) is the price of the sweatshirts Analyzing this model involves answering the following questions: #### A) Determine the Price Elasticity of Demand (E) when the Price is set at $20. SHOW WORK. To determine the price elasticity of demand (E), we use the formula: \[ E = \left(\frac{dQ}{dp}\right)\left(\frac{p}{Q}\right) \] 1. Calculate \( \frac{dQ}{dp} \): \[ q = -p^2 + 33p + 9 \] \[ \frac{dq}{dp} = -2p + 33 \] 2. Substitute \( p = 20 \) into \( q \): \[ q = -(20)^2 + 33(20) + 9 \] \[ q = -400 + 660 + 9 \] \[ q = 269 \] 3. Substitute \( p = 20 \) into \( \frac{dq}{dp} \): \[ \frac{dq}{dp} = -2(20) + 33 \] \[ \frac{dq}{dp} = -40 + 33 \] \[ \frac{dq}{dp} = -7 \] 4. Calculate E: \[ E = \left(\frac{dQ}{dp}\right)\left(\frac{p}{Q}\right) \] \[ E = (-7)\left(\frac{20}{269}\right) \] \[ E \approx -0.52 \] #### B) Is demand elastic or inelastic at a price of $20? What will happen to revenue if we raise prices? Explain. Given \( |E| \approx 0.52 \) (which is less than 1), the demand is inelastic. **Explanation:** - If the price increases, the percentage decrease in quantity demanded will be smaller than the percentage increase in price. - Hence, raising prices will increase total revenue
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS