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I'm working on a algebra exercise and need a sample draft to help me study.

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MAT 171 Lab – Break Even Point (Supply and Demand)
Modified from Pearson Engaging Algebra Projects
The Writing Place Pen Factory is in the process of manufacturing a new type of ball point pen.
Precise records are kept concerning the production costs for each week. The production supervisor,
George, supplies the following table to Terry, the account manager.
Week #
Number of Pens Produced
Total Cost of Production
1
2500
5800
2
3600
3600
3
5000
4150
4
4000
3700
5
9250
5420
6
8400
4850
7
6500
4230
1. Use your graphing calculator to make a scatter plot of the data.
a. What does the graph seem to indicate concerning the production costs during the first
week?
b. Using the linear regression feature on your calculator, fit a linear function using the entire
data set. Write out the equation of best fit and give the 𝑟 2 value. Round to 2 decimal places.
c. Does this 𝑟 2 value show the line being a good fit for the data? How do you know?
d. Use your graphing calculator to graph this line of best fit on the same plane as the scatter
plot. Does the line appear to be a good fit for the data? How do you know?
2. Using the linear regression feature on your calculator, fit a linear function to the data, excluding
the data from the first week. Write out the equation of best fit and give the 𝑟 2 value. Round to 2
decimal places.
3. Compare the 𝑟 2 values from numbers 1b and 2. Which of these functions (1b or 2) is a better fit
for the data? Should the data from the first week be used when trying to determine the cost equation
for production? Explain your answer.
a. Using the line of best fit from number 3, write a cost function C(x), for the data set. (Hint:
describe the weekly cost, C(x), as a function of the number of pens produced, x).
b. What is the slope of the cost function? In terms of this data, what does the slope represent?
c. What is the y-intercept of the cost function? In terms of the data, what does the y-intercept
represent?
4. Julie, the sales manager for The Writing Place, Inc, has determined that the optimum selling price
per pen is 59 cents. Use this amount to complete the table below.
Number of Pens Sold
2500
3600
5000
4000
9250
8400
6500
Total Revenue
a. Find the equation that describes revenue as a function of the number of pens sold.
b. What is the slope of the revenue function? Interpret this slope in terms of the data.
c. What is the y-intercept of the revenue function? In terms of the data, what does the yintercept represent?
5. Use the cost function from 3a and the revenue function from 4a to answer the following questions:
a. Find the revenue when 4000 ball point pens are sold.
b. Find the cost for producing 4000 ball point pens.
c. Is there a profit or loss when 4000 ball point pens are produced and sold? How do you
know?
d. Find the revenue when 9000 ball point pens are sold.
e. Find the cost for producing 9000 ball point pens.
f. Is there a profit or loss when 9000 ball point pens are produced and sold? How do you
know?
6. Using your graphing calculator, graph the revenue function (from part 4a) and the cost function
(from part 3a) on the same graph. (Hint: Use 𝑦1 for cost and 𝑦2 for revenue). Find the point of
intersection for these two lines. This is the break-even point. What is the ordered pair for the breakeven point?
a. How many ball point pens should be produced and sold to break even?
b. What is the value for costs and revenue at the break-even point?
7. What advice would you give George regarding the production level of ball point pens?
8. What advices would you give Julie concerning the sales of ball point pens?
...

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