Systems of Equations and Inequalities

Systems of Equations and Inequalities

Dr. Molli Jones, PA3-MSP Year 3

Activity 1: Suit Yourself

http://www.nasa.gov/audience/foreducators/exploringmath/algebra1/Prob_SuitYourself_detail.html

Creating Linear Equations

Solving Systems of Linear Equations

Activity 2: Activities for Learning to Solve Systems of Equations

http://www.ehow.com/info_8620875_creative-ways-teach-systems-equations.html

http://www.ilovemath.org/index.php?option=com_docman&task=doc_details&gid=11

Connecting Equations with their Graphs

Utilizing Multiple Methods for Solving Systems of Equations and Inequalities

Solving Mixture Problems Presented in a Variety of Formats

Activity 3: Linear Programming – A Potato-Head Business Adventure

Solving Systems of Linear Inequalities

Mathematical Modeling

Activity 4: Exploring More Advanced Systems with NASA Examples

http://spacemath.gsfc.nasa.gov/weekly/6Page156.pdf

http://spacemath.gsfc.nasa.gov/weekly/3Page8.pdf

Systems of Three Equations with Three Unknowns

Quadratic Systems of Equations

Activity 2: Activities for Learning to Solve Systems of Equations

Treasure Hunt

Goal: Understand the connection between equations and their graphs.

Rules: Each group will be given a pair of equations. The group will use any method to solve the system of equations, and then locate their treasure based on the solution to the system. The group may only take the treasure that matches their system of equations.

Secret Agents

Goal: Understand the usage of different methods to solve systems of equations.

Rules: Our group of secret agents has been infiltrated with spies, and it is your job to determine the spies. We have received intelligence regarding a list of equations that can be used to determine the spies. Any participant whose number is a solution to a pair of equations from the list is a spy. Each team of secret agents will be assigned a specific method to use so that the work can be kept secret. The first team to find all of the spies wins a reward.

Candy Jar

Goal: Use systems of equations to solve real-world problems.

Rules: A candy jar has been placed in the room. You will be given problems about the candy in the jar. If you can answer the questions about the jar correctly, you will be allowed to take a piece of candy.

Activity 3: Linear Programming – A Potato-Head Business Adventure

Linear programming is a tool for solving optimization problems, problems where you are trying to minimize or maximize a quantity based on a set of constraints.

A manufacturer makes bikes and wagons. To produce a bike requires two hours on Machine A and four hours on Machine B. To produce a wagon requires three hours on Machine A and two hours on Machine B. Machine A can operate at most 12 hours per day, and Machine B can operate at most 16 hours per day. If the manufacturer makes a profit of $12 per bike and $10 per wagon, how many of each should be produced in order to maximize profit?

The first step is to organize the information:

Machine A / Machine B / Profit
Bikes
Wagons
TOTAL / MAXIMIZE

Next, we need to use this information to create the mathematical model of the situation.

·  Decision Variables - There will be two of these, and they represent the decision to be made.

·  Objective Function - This is the function that you want to maximize or minimize.

·  Constraints - The inequalities that limit the objective function.

·  Sign Restrictions - Indicate what values the decision variables can have.

Now, graph the inequalities and find the corner points of the feasible region. Once you have the points, plug each corner point into the objective function. We are looking for the point that gives us the maximum value.

State your conclusion.

Potato Head Division

Hasbro Toys

1027 Newport Avenue

Pawtucket, Rhode Island 02862

August 1, 2012

PA3-MSP Math Participants

Immaculata University

1145 King Road

Immaculata, PA 19345

Dear Mathematics Teachers:

I currently work for the Potato Head Division of Hasbro Toys. I am charge of deciding which accessories we should include in the upcoming version of Mr. Potato Head. Our marketing team has come up with two great ideas for this super-hero themed version, but it is my decision what we will end up manufacturing.

The first version that we could manufacture would be Superspud, which would be a Superman version of Mr. Potato Head. The other possibility would be Spuder-Man, which would be a Spider-Man version of the toy, although I personally think the name could use a little work. The table below includes information about what each play set would contain.

Our marketing department feels that we can sell Super Spud for $14.99 and Spuder-Man for $12.99, but they think that we can sell up to twice as many Spuder-Mans as Super Spuds. Our workers on the production line get paid $12.00 per hour. We have 50 workers that work 40 hours per week.

Super Spud / Spuder-Man
Part / Materials
(cents) / Labor
(seconds) / Part / Materials
(cents) / Labor
(seconds)
Body / 30 / 10 / Body / 30 / 10
X-Ray Vision Eyes / 15 / 2 / Spider-Shaped Eyes / 15 / 30
Nose / 5 / 2 / Spider Mask / 20 / 60
Mouth / 5 / 2 / Red Web-Slinging Arms / 20 / 10
Ears / 10 / 2 / Red Spider Stockings / 15 / 30
Flying Position Arms / 20 / 10 / Web / 5 / 30
Red Boots / 15 / 2 / Spider Tracers / 15 / 30
Black Molded Hair / 15 / 2 / Camera / 5 / 2
Cape / 20 / 15
Chest Emblem / 15 / 30
Kryptonite / 40 / 8
Lead Box / 50 / 15

In order to maximize our profits, how many Spuder-Mans and how many Super Spuds should we make in a week? Please clearly explain your calculations so that I can relay this information to my boss. Thank you for your help.

Sincerely,

Spud Russet