PRESENTATION TITLE
Maximizing Critical Thinking via Algebra
CMC – South 2015
Roberto Soto
November 7, 2015

A recent school play at Desert High School broke attendance and revenue records. There were 75 tickets sold for a total of $585. If parent tickets were sold for $12 and student tickets were sold for $5, how many parents and how many students attended the play?

• Make sense of problems and persevere in solving them
• Reason abstractly and quantitatively
• Construct viable arguments and critique the reasoning of others
• Model with mathematics
• Use appropriate tools strategically
• Attend to precision
• Look for and make use of structure
• Look for and express regularity in repeated reasoning.

• Critical Thinking
To analyze and evaluate information in order to make a decision and/or form an opinion.
• Linear Programming
A method of solving optimization problems using linear algebra.

Company A has determined that the cost of producing a smartphone is $350 and the cost of producing a tablet is $450. Company A has also determined that it takes 1 labor-hour to produce a smartphone and 2 labor-hours to produce each tablet. The profit on a smartphone is $100 and
$150 for each tablet. If their factory has a capacity of 120 labor hours per day and Company A would like to keep their costs per day under $31,500, how many of each product should it produce in order to maximize profit?

Let x = the number of smartphones that
Company A will produce
Let y = the number of tablets that Company A will produce

Graph created by Desmos.com

A department store has up to $20,000 to spend on television advertising for a sale. All ads will be placed with one television station. A 30-second ad costs $1000 on daytime TV and is viewed by 14,000 potential customers, $2000 on prime-time TV and is viewed by 24,000 potential customers, and $1500 on late-night
TV and is viewed by 18,000 potential customers. The television station will not accept a total of more than 15 ads in all three time periods. How many ads should be placed in each time period in order to maximize the number of potential customers who will see the ads? How many potential customers will see the ads? (Ignore repeated viewings of the ad by the same potential customer.)
from Finite Mathematics for Business, Economics, Life Sciences, and Social Sciences, 12th edition, by Raymond Barnett, Michael
Ziegler, and Karl Byleen.

Let x = the number of daytime ads
Let y = the number of primetime ads
Let z = the number of late night ads

Plot created using Mathematica

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2000 15
0 40/3 0 5/3
0 15 -2500 0
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15 0 -10,000 0
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240,000
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240,000
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210,000
230,000
260,000

• Simplex Method – Standard Maximization
Problem by Brian Veitch https://youtu.be/XK26I9eoSl8
• The Simplex Method in Excel
– Video
– Adding Solver to Excel

• Handouts for this talk
• Scaffolding to this topic
• Sample written work

• Class Project – “Bake” Sale
– Determine what to sell in order to maximize profit.
– Use surveys to determine appropriate prices.

Roberto C. Soto, PhD
CSU Fullerton rcsoto@fullerton.edu
(657) 278-2743 http://math.fullerton.edu
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