Microworld: Introduction
to Linear Programming
Click the Hyperlink
above to visit the Microworld.
Author:
Ravinder
Kumar
The
seeds of linear programming were sown during world
war II when the military supplies and personnel had to be moved efficiently.
Linear programming deals with optimization. Although linear programming problems
can be very complicated, which is expected, since they are real-world problems,
we will start with simple problems that can be solved at an elementary algebra
(college algebra, precalculus) level. Below we give an example of the kind
of linear programming problem that you will be able to explore and solve.
Then we continue to discuss the simplex algorithm.
Joe
assembles two types of cameras, the excelerio and the premerio. His cost of
assembling these cameras is $21.00 and $42.00 respectively. The total funds
available for his use are $1,260.00. It takes 5 hours to assemble an excelerio
and 2 hours to assemble a premerio. He can work for no more than 100 hours.
If the profit on the two kinds of cameras is $8.00 and $10.00 respectively,
determine how many cameras of each kind Joe should assemble to earn maximum
profit.
This
12-page microworld is aimed at a range of different levels. Solution of inequalities
and of systems of inequalities can be studied at Intermediate Algebra and
College Algebra. Solving systems of equations and linear programming problems
in two unknowns using geometrical methods can be studied at the College Algebra
and Pre-Calculus levels.
Solving
systems of equations and the Simplex Algorithm can be studied at Linear Algebra
level. Originally, this microworld was aimed at College Algebra and Pre-Calculus
levels. That is why it started from a very elementary consideration of what
an inequality is, and how to solve an inequality or a system of inequalities.
Once
we began solving linear programming problems using a geometrical method, it
was natural to develop the simplex algorithm. We have considered only standard
linear programming problems, although page 10 can be used to manually solve
nonstandard problems also.
However,
automating the simplex algorithm on pages 11 and 12 is really geared towards
standard linear programming problems. It is our intention to follow up this
microworld with another microworld, which would consider the nonstandard case.
We believe that it will be appropriate to call such a work “dantzig”.
This
Microworld contains two types of online Help. Most pages contain the mathematical
explanations under the "Help for this page" button. The simplex
algorithm needs to be considered in special detail. So, you may click the
button “Math for this page” on pages 10 and 12 for an in-depth explanation
of the Simplex Algorithm.
This
book may be used for
- Intermediate algebra and College Algebra
- Precalculus
- Linear Algebra
Number
of Pages: 12
Animation: Yes
Grade Level: 11-15
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