Getting the Most for Your Money

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Grade Level: High School Juniors and Seniors

Lesson Designer: Breanne Oldham

Algebra II Standard:

2.0 Algebra:  Students will describe, extend, analyze, and create a wide variety of patterns and functions using appropriate materials and representations in real-world problem solving, and will demonstrate an understanding of the behavior of a variety of functions and their graphs.

Learning Expectation

2.14  use linear programming to solve real-world problems.

State Performance Indicators:

  • sketch a system of linear inequalities and determine the maximum or minimum value of the related function

  • find the maximum or minimum value given the graph of the feasible region of the real world linear programming application

Materials Needed:  One computer per group, Excel, Word, printer

Duration of the Lesson: 2 blocks (total of 3 hours)

Scaffolding Activities
Complete the scaffolding activities to the right by clicking on each link and completing the given assignment. 

If you get to a math concept that you can't remember how to do check out SparkNotes.com and choose the appropriate link.

Word Scaffolding Activity

Excel Scaffolding Activity

Remind yourself of the difference in area and volume and what they are by clicking here and reading the appropriate sections.

Area

Volume

The Problem:

You work part time in an office.  Your office needs new vertical filing cabinets of at least 4 drawers that will maximize the storage space available while still fitting within your budget restrictions.  You have 60 square feet of floor space for the cabinets and $600 to spend.  Your boss has tasked you with solving this problem since she knows that you are taking Algebra II and have been studying linear programming.  As an added incentive, if you do well, she will recommend that you get a raise. 

What do you do?

 
Your Instructions:
  1. Research vertical filing cabinets with at least 4 drawers using the websites following these instructions.  Choose a total of 5 different filing cabinets from at least 2 different suppliers (different colors do not count as different filing cabinets).  In Word, make a table showing the company, the filing cabinet, the floor space it will take up, the total storage space gained, and the price.  If you need to do scratch work to find floor space and total storage space, do it on a separate sheet of paper. (Knowledge, Comprehension)
  2. Limit your choices to 2 filing cabinets.  Show your choices by bolding them in the table. (Application, Analysis)
  3. Write a linear programming problem, including constraints and an objective function.  Place your linear programming problem in the Word document under your table. (Knowledge, Analysis)
  4. Graph your problem in Excel.  Copy your graph to the Word document. (Knowledge, Comprehension)
  5. Using your graph, analyze the results to determine how to get the most for your money.  Round intersections to the nearest whole number since you must buy whole filing cabinets.  Your scratch work may be done on a separate sheet of paper.  Type your final results into the Word document. (click here for an example). (Analysis)
  6. Write a paragraph of at least five complete sentences justifying your answer.  In your paragraph, include your reasons for limiting the choices to the two that you picked and why you recommend the filing cabinet that you choose. (Evaluation)
  7. Print your final Word document.  Staple your scratch work paper to it and turn in.
 
Websites

Staples

Office Max

Quill

 

Here is an example of the Word Table

Company

Filing Cabinet

Floor Space

Storage Space

Price

Office Depot

Office Designs High-Side Metal File, 4 Drawers, Putty

≈ 1.8 sq. ft.

≈ 6.9 cubic ft

$99.99

Office Depot

Office DepotŪ 4-Drawer Vertical Letter File, Black

≈ 2.8 sq. ft

≈ 11.6 cubic ft.

$119.99

 

Assessment:

Click here to see the grading rubric for this assignment