The Official SAT Question of the Day

Friday, September 30, 2011

Moving Toward Linear Programming and Simultaneous Equations

MIT SEED applications are now being accepted!  All interested students should come see me.  An amazing opportunity and one that should not be passed up!

Precalculus will be completing their application of inverse matrices to solve "traditional" and "non-traditional" three variable system word problems and then move onto an eight day exploration of linear programming.  The image to the left shows a system of inequalities that represents the constraints on two variables.  The region that is darkest represents all the possible, feasible, values that "work" given the five different constraints.  The vertices of the polygon of the "feasible region" give the maximum and minimum values given the constraints.  We will primarily use these maximum and minimum values to solve business related problems that require us to determine what will maximize profit and/or minimize cost.

Here is an example problem from the Transition Mathematics Project:
Your great aunt left you a trust fund of $18,000 that you may now have to invest with some restrictions.  You have three different funds from which to choose.  The municipal bond fund has a 5.26% return, U.S. Bank has certificate of deposits (CDs) with a 2.25% return and the high-risk fund has an expected (but not guaranteed) return of 9%.  To minimize risk, you decide to invest a maximum of $3,000 in the high-risk account.  A stipulation of the trust indicates that you must invest at least three times as much in the bank CDs as in the municipal bonds.  Assuming the year-end returns are as expected, what are your best investment choices to maximize your return?  Be sure to state how much you will invest in each fund. 
You will be able to solve this!

Homework is due in two weeks!  A great deal of graphing and interpreting is involved so work steady and check-in with me regularly.Here is the link to the chapter from which the problem set came.
Please find the slides related linear programming here as well and some exemplar problems to help guide you on your way.
Slides: Text Examplars: Homework

Video resources:
Brightstorm Videos on solving and graphing inequalities
Khan Academy on graphing inequalities
Youtube Video 1 on Linear Programming
Youtube Video 2 on Linear Programming

Algebra II will quickly cover lines and move directly into classic system of equations problems.  The aim here will be twofold:  review of all things linear and translation of word problems.  We will continue to keep midpoint and distance formulas as well as exponents and radicals in play as much as possible by reviewing with Tarsia triangles, hexagons, and dominoes (see image of completed Tarsia triangle at left).

Slides: Homework (from University of Houston): Linear Equations Reference Sheet

Brightstorm Videos:

These videos are aligned to the sections from your textbook, so as you are completing homework from your textbook you can easily locate the most relevant videos for you!

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