Mat 211 ASU Homework 2.2

Set up and solve these two systems to the right of the text box.  I have started these for you. 

You may type in values for your [C] and [R] matrices.

Everything else MUST be calculated in Excel!

w + x + y + z = 4

w - x + y + z = 3

w + x - y - z = 0

w             - z = 0

A + B - C = 0

B + C - D = 0

C + D - E = 0

A - B = 0

D + E = 8

Here are some simple arrays for you to set up and then operate on as indicated.

Start by inverting [A] below right.

Then generate the original [1 ´ 3] arrays along Columns O-Q from the arrays defined in Columns K-M.

Finish by producing the Columns S-U arrays.

Save!

You are going to have to  fix the last two equations on your own paper first before entering their coefficient and RHS values along the 3rd & 4th rows in [C].  Type in the coefficient values as applicable for the 1st row in [C], but then combine in Excel (via multiplication) your first row's values with their respective italicized numbers above each (Cells K4-Q4).  Then finish the problem.

At the right is a one-step transition matrix of 7 system states which correspond to the floors in the Goldwater building (GWC) on the Tempe campus.  These data are partially based on a study that Mr. Ulrich performed for one of his classes (Intro to OR) as a part of his doctoral studies.  Data were gathered at 10-second intervals which is why some floors appear to be able to "revisit" themselves.

Determine the steady state matrix for this system, pasting each subsequent higher-order transition matrix sequentially below its predecessors (similar to as we had performed with the GEN101 HW assignment's graphs).  Make sure to use the macros and processes as have been taught to you; however, do not worry about keeping track of the order (power) of the first steady state matrix.

Report final probabilities to four decimal places.

1) Report below which floor has the highest probability of being visited in the long run, as well as what that probability is:

Answers Here ® In the long -run, "First" floor has the highest probability  of reaching at 0.4661

1) Report below which floor has the lowest probability of being visited in the long run, as well as what that probability is:

Answers Here ® The "Fourth" floor has the lowest probability in the long-run at 0.0396

3) This study came about because Mr. Ulrich used to perform grad research work as a student many years ago . . . Our lab was on the 5th Floor, and our contention was that people on the first three floors "hogged" the front two elevators.  If we assume that the data at the right represent an amalgamation of both front elevators, is the above contention supported?  Why or why not (include data from your steady state matrix in your response)?

Briefly Answer Starting Here ®