Subject: General Questions    / General General Questions

Module 4 – SLP

LINEAR PROGRAMMING

Complete the wrapup of a three-round Delphi decision-making exercise, following the detailed example cited in the Home Page discussion. As before, you may copy and / or adapt verbiage from the example without citing it.

SLP Assignment Expectations

The SLP writeup should consist of:

The Letters to the Participants, which include

Thanks for their participation

A summary of their third-round responses

A short narrative discussing the evolution of the decision-making process, how opinions shifted, what relevant factors the group identified, and what consensus (if any) the group arrived at.

Follow the instructions in the BSBA Writing Style Guide (July 2014 edition), available online at

https://mytlc.trident.edu/files/Writing-Guide_Trident_2014.pdf.

There are no guidelines concerning length. Write what you need to write – neither more, nor less.

In the SLP ONLY, references and citations are NOT required. However: If you state a fact, express an opinion, or use a turn of phrase that isn’t your own, then you should credit the source, just like you would in everyday conversation. (Example: “In the words of Monty Python, ‘And now for something completely different.’ “)

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TEST YOUR UNDERSTANDING: Answer

The linear equations corresponding to the constraints are:

1. 2y = 3x

2. 2x + 3y = 15

3. 3y = x

Here’s the plot, with the lines, extrema, and the region labeled. It was created with Relplot, and the labels were added using the Snagit graphics editor. Using Relplot, it’s possible to create the sketch without knowing the coordinates of the extrema. That’s because the app takes the line equations as input.

Here’s another version. It’s less elaborate, but still perfectly acceptable. If you want to upload a hand sketch, however, you’ll have to do the calculations first, so you’ll know where to put the extrema.

Here’s how to find the coordinates of the extrema:

A: The only values of x and y that satisfy the equation 1 (that is, 2y=3x) is (0,0) . Ditto for equation 3. So the coordinates for A are

A(0,0)

B: This point is the simultaneous solution of equations 1 and 2; that is, of

2y=3x

2x + 3y = 15.

We’ll use the Webmath solver (Discovery, 2014) to find the values of x and y that satisfy both equations. There are many such apps on the Web; look for them using Google, or your favorite search engine.

Here’s what the setup looks like:

Proceed in the same way to find the coordinates of point C, which is simultaneous solution of equations 2 and 3; that is,

2x + 3y = 15

3y=x

The answer is C(5, 1.67).

Summary answer: Extrema are

A(0,0)

B(2,31, 3.46)

C(5, 1.67)

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