PLEASE answer all questions OR  answer 10-20 The marching band at a local high school is selling candy bars. The profits will go toward the purchase of new marching band uniforms. They are interested in knowing what price they should charge to obtain the maximum profit. The candy bars are donated by a local retailer so they know that if they charge $0 they will make $0 profit. They also collect data from other marching bands who have sold candy bars in the past. The data they collected is shown in the table below. Price 0.00 0.45 0.60 0.75 1.00 1.25 1.40 1.50 Profit 0.00 $720 $900 $990 $845 $625 $560 $300   What factors might influence how much is to be made from the candy sale? Give at least two. What happens to the profit as the price of each candy bar increases Explain possible reasons for your observations. How do you suppose the other bands determined the price at which to sell each candy bar? Do any data values seem unusual? Yes     or        No       (circle one) Why? Which quantities do the independent and dependent variables represent? Independent variable:  Dependent variable: Draw the scatterplot of the data. Sketch the graph below. Label both axes with what each represents as well as a numerical scale. Does the relationship look linear or quadratic? Using your graphing calculator, find the model (equation) that represents the  line or curve of best fit. Write it here. Accurately draw the curve on the graph of the scatterplot that you drew for #6. Find the vertex and intercepts of your model. Does the curve look like a good model? Circle one:     Yes    or   No Predict the profit if they charge $1.75 for each candy bar. Is this interpolation or extrapolation? Does it make sense? Show work. Profit: ____________________                          Circle one:   Extrapolation             or        Interpolation Does this prediction make sense?          Yes     or        No Why or Why not? Predict the profit if they charge $1.15 for each candy bar. Is this interpolation or extrapolation? Show work.  Profit: ____________________  Circle one:         Extrapolation     or    Interpolation Find the price the band should charge to obtain the maximum profit. What is the profit? Think about where the maximum occurs for a quadratic function. Show work. Price: ____________________    Profit: ____________________

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...
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PLEASE answer all questions OR  answer 10-20

The marching band at a local high school is selling candy bars. The profits will go toward the purchase of new marching band uniforms. They are interested in knowing what price they should charge to obtain the maximum profit. The candy bars are donated by a local retailer so they know that if they charge $0 they will make $0 profit. They also collect data from other marching bands who have sold candy bars in the past. The data they collected is shown in the table below.

Price

0.00

0.45

0.60

0.75

1.00

1.25

1.40

1.50

Profit

0.00

$720

$900

$990

$845

$625

$560

$300

 

  1. What factors might influence how much is to be made from the candy sale? Give at least two.
  2. What happens to the profit as the price of each candy bar increases Explain possible reasons for your observations.
  3. How do you suppose the other bands determined the price at which to sell each candy bar?
  4. Do any data values seem unusual? Yes     or        No       (circle one) Why?
  5. Which quantities do the independent and dependent variables represent?
  6. Independent variable:  Dependent variable:
  7. Draw the scatterplot of the data. Sketch the graph below. Label both axes with what each represents as well as a numerical scale.
  8. Does the relationship look linear or quadratic?
  9. Using your graphing calculator, find the model (equation) that represents the  line or curve of best fit. Write it here.
  10. Accurately draw the curve on the graph of the scatterplot that you drew for #6. Find the vertex and intercepts of your model.
  11. Does the curve look like a good model? Circle one:     Yes    or   No
  12. Predict the profit if they charge $1.75 for each candy bar. Is this interpolation or extrapolation? Does it make sense? Show work.
  13. Profit: ____________________                         
  14. Circle one:   Extrapolation             or        Interpolation
  15. Does this prediction make sense?          Yes     or        No Why or Why not?
  16. Predict the profit if they charge $1.15 for each candy bar. Is this interpolation or extrapolation? Show work.
  17.  Profit: ____________________
  18.  Circle one:         Extrapolation     or    Interpolation
  19. Find the price the band should charge to obtain the maximum profit. What is the profit? Think about where the maximum occurs for a quadratic function. Show work.
  20. Price: ____________________    Profit: ____________________
Expert Solution
Step 1: Q10)

Q10) . 

Equation of best fit quadratic curve = -1373.8x2 + 2266.2x + 4.9755

 

vertex : (0.8348, 939.548)

x-intercepts: (-0.0022,0) and (1.6518,0)

y-intercept: (0,4.976)

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