Simplest 1.0 demo is a full featured version of the program only limited to a small number of variables and constraints. This brief document explains enough to use the program and know its main features.
The full workable version comes with a complete written documentation and data examples. You can get Simplest 1.0 by sending $45.00 directly to the author:
Benito M. Villamarín
2 Soldiers Field Pk #721
Boston, MA 02163
The above fee will also allow you to receive free upgrades of the program.
What is Simplest?
Simplest is a linear programming application for the Apple Macintosh. Its main features are:
• Works with Macintosh 512E, Plus, SE and II.
• Can solve linear programs of up to 250 variables by 250 constraints, depending on the available memory.
• Very fast.
• High accuracy by using SANE.
• Open files in three different formats.
• Support the ImageWriter I and II and the LaserWriter printers.
• Color printing in the Imagewriter II.
• Built-in text editor.
• Allows to save and print the initial and final tableaus.
• Optional information in every iteration.
• Numerical output in fixed or floating point.
• Memory management to accommodate to the more critical circumstances.
• Reconfigurable maximum dimensions.
• Color in the Macintosh II
• Multifinder compatible. Can work in the background.
How to prepare a input file
Simplest accept file in three different formats:
- Equations (text)
- Table (text)
- Compact (binary)
The compact format is created by the own program. It is shorter and faster to read. The other two format are text files that you can create inside or outside the program.
A file in equations format is nothing more than a text file containing the standard description of a linear program, i.e.:
max 3 x1 - 2 x2
subject to
x1 + 3 x2 <= 7
2 x1 - x2 <= 5
end
There are three key words that should be always present:
- MAX (or MIN)
- SUBJECT TO
- END
It does not matter uppercase or lowercase.
You may include the name of the constraints as follows:
max 3 x1 - 2 x2
subject to
y1: x1 + 3 x2 <= 7
y2: 2 x1 - x2 <= 5
end
The names of variables and constraints have to begin with a letter and may no contain more than 8 characters. The set of permissible characters to form the names is composed only of: the letters, the numbers and the underscore '_'. (Be specially careful about do not using the dash or minus sign).
The relational signs may be one of the following: =,<=,>=,<,>,≥,≤.
After the objective function and after each constraint you should type a return. You may include all the spaces that you want.
The text file can be edited using the built-in text editor or you may use some other wordprocessor to edit the text, but in this case you should save the file as text only.
How to solve a linear program
You use the Open text... item in the File menu to open the text file that you created previously, or the Open item to open a file previously saved as compact (as the example file provided). The text appear in the built-in editor's window where you may always introduce changes and save them. After that you have to validate your input file using the Validate item of the Do menu. The program scan through your input file and pass the data to memory or report you some error. If the program does not detect any error, a new window appears containing a summary description of your input data. You may look at your data using the items under the Window menu: Variables, Constraints and Matrix, new windows will appear in these cases. If you wish to change your problem in some way you should come back to the editor window using the Modify item of the Do menu.
To go ahead in solving the problem use the Solve item under the Do menu. In the main window you will see the progress of the solving task, in terms of time, number of iterations and value of the objective function. The program can solve the problem in the background when working under Multifinder. Finally it will indicate whether the linear program is feasible, infeasible or unbounded.
You have always the possibility of aborting the resolution by typing a period while pressing the Command key.
More information is available during the solving process if you check previously the Info in all pivots item in the Options menu. In that case other window will show you which variables leave and enter the basic solution.
In the case that the problem is feasible, the solution will be displayed on the Variables and Constraints windows. After that, you also may perform a sensitivity analysis on the objective function and the right hand side using the corresponding items of the Do menu.
Simplest will inform you if there exist another optimal solution, and in that case you can compute it by using the Another item under the Do menu.
There are many other features of the program that are covered in detail in the documentation that comes with the full featured version of the program.
