Option #1: Finding the Break-Even Point
For this Critical Thinking assignment, you will investigate profits using systems of equations.
Part I: Complete the following steps:
1. Read Example 10 in Section 9.1 of Precalculus.
2. Use the GeoGebra tool to graph the cost and revenue functions given in Example 10.
3. Identify the break-even point using the “Intersect” tool under “Points”.
4. Save your GeoGebra work as a .pdf file for submission.
Part II: Based on your work in Part I, discuss the following:
1. Discuss the part of the graph that represents the profit.
2. Discuss how you found the break-even point on the graph.
3. If you are performing a break-even analysis for a business and their cost and revenue equations are dependent, explain what this means for the company’s profit margins.
4. If you are solving a break-even analysis and get more than one break-even point, explain what this signifies for the company?
5. If you are solving a break-even analysis and there is no break-even point, explain what this means for the company.
6. How should they ensure there is a break-even point?
7. Solve the following problem: An investor earned triple the profits of what she earned last year. If she made $500,000.48 total for both years, how much did she earn in profits each year?
a. Write an analysis of your solution to this problem similar to the one included at the end of Example 10.
b. Describe the graph that could model this situation.
c. Discuss how your answer would be affected if:
i. The amount earned for both years was increased.
ii. The investor only earned double the profits of what she earned last year.
Discussion may include: On the graph, the region of profit will be where the revenue function values are higher than the cost function values. The break-even point will be the intersection points of the two graphs. Having more than one break-even point means that there are alternations of profit and loss. Dependent equations would mean they are the same curve and no profit exists. If there is no break-even point, then either there was continuous profit or there was continuous loss.
You must submit two files for this assignment. The first file should contain the computations, graphs, diagrams, etc., associated with the questions in Part I. This file may be formatted as a numbered list of answers. Unless stated in the problem, a narrative discussion is not required, but you must provide enough information to show how you arrived at the answer.
The second file should be a 2-3 page narrative paper, written in APA format, associated with the situation described in Part II. Specific requirements for the paper are provided below:
a. Your paper should be 2-3 pages in length (not counting the title page and references page) and cite and integrate at least two credible outside sources.
b. Include a title page, introduction, body, conclusion, and a reference page.
i. The introduction should describe or summarize the topic or problem. It might discuss the general applications of the topic or it might introduce the unique terminology associated with the topic.
ii. The body of your paper should address the questions posed in the problem. Explain how you approached and answered the question or solved the problem, and, for each question, show all steps involved. Be sure this is in paragraph format, not numbered answers like a homework assignment.
iii. The conclusion should summarize your thoughts about what you have determined from your analysis in completing the assignment. Nothing new should be introduced in the conclusion that was not previously discussed in the body paragraphs.
c. Include any tables of data or calculations, calculated values, and/or graphs referenced in the paper. (Note: The minimum required length excludes any tables, graphs, etc.)