# Linear Programming Modeling Examples

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```					For Problem 17 below, solve the linear programming model by using the computer. You can use
either QM for Windows or Solver (in Excel) to solve this problem.

If using QM for Windows, you can capture the results and a graph in one of two ways:

   By doing a “Print Screen,” you capture the screen image. You can now copy directly to
the Word document (or to Paint, and then to Word).
   Or you can save data from QM for Windows as an HTML file. You can only save data
one window at a time. Highlight the QM for Windows output window you want to save
and select Save As HTML. You can then edit the HTML file in Word to your liking, or
you can copy it directly to Word.
   Do not send an HTML file, or a JPEG file.

If you use QM for Windows, please include the original problem plus results screen in the Word
document you create. Include the model formulation or a window showing the constraints. Save
the resulting file as a Word file.

If using Solver, please submit the Excel file (include the model formulation on the worksheet).
If using an Excel document, put one problem per worksheet, label all worksheets and put all
problems in one file.

Please read problem statements carefully to distinguish between a maximization problem and a
minimization problem. Include both model formulation and computer solution.

Problem 17 (Linear Programming: Modeling Examples)

Lawns Unlimited is a lawn care and maintenance company. One of its services is to seed new
lawns as well as bare or damaged areas in established lawns. The company uses three basic
grass seed mixes it calls Home 1, Home 2, and Commercial 3. It uses three kinds of grass seed-
tall fescue, mustang fescue, and bluegrass. The requirements for each grass mix are as follows:

Mix                           Mix Requirements

Home 1                No more than 50% tall fescue
At least 20% mustang fescue
Home 2                At least 30% bluegrass
At least 30% mustang fescue
No more than 20% tall fescue
Commercial 3          At least 50% but no more than 70% tall fescue
At least 10% bluegrass

The company believes it needs to have at least 1,200 pounds of Home 1 mix, 900 pounds of
Home 2 mix, and 2,400 pounds of Commercial 3 seed mix on hand. A pound of tall fescue costs
the company \$1.70, a pound of mustang fescue costs \$2.80, and a pound of bluegrass costs
\$3.25. The company wants to know how many pounds of each type of grass seed to purchase to
minimize cost.
a. Formulate a linear programming model for this problem.
b. Solve this model by using the computer.

```
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