Applied Linear Algebra

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(c)2017 Second Wind Productions, LLC

(c)2017 Second Wind Productions, LLC

There are 350 examination points on this test, worth 35 CPs. This is the only document on which you will be working for this examination for required points. Points per worksheet are defined in each worksheet's tab. There are two additional documents which are an extra credit opportunity. As a minimum, you will need to turn in the Excel BL file for some points. Max points are only possible with both files submitted (and, of course, correctly completed). Make sure to appropriately rename the files by replacing Name in each filename with your last name plus immediate first initial. However, unlike other assignments, if you do not appropriately rename the file, I will still accept it for grading but you will automatically lose 15% of your points. Consequently, it is in your best interests to let me look at your file before you submit it if you have any questions at all, including its filename. Make sure to also follow my formatting instructions. As stated in the GEN101 activities and documents:  If you correctly format the cells but have a wrong answer, some partial credit is likely, but  If you incorrectly format the cells, then it won't matter whether you performed the calculations correctly: It's wrong! Again, feel free to email should you have any questions; please remember to identify your course in the email subject line, and to also attach a current copy of your examination. Make sure to NOT type in any values where calculations are required, which is just about everywhere. I will let you know when you may type in a value.  IF you type a value directly into any cell not authorized by me, then you will lose ALL points for that worksheet; however . . .  If you do this on two or more worksheets, then you will might receive a zero for the entire examination. Again, if you are unsure about this or anything else anywhere in the examination, email me. DUE BY 2359 HOURS ON FRIDAY, 04/27/18

EX2-1 115

(c)2017 Second Wind Productions, LLC

(c)2017 Second Wind Productions, LLC

Emerald City has five purification plants: P(lant)1-P(lant)5. Their costs to process each million (1E6) gallons of sewage and their resulting purification levels are shown in the table below. Pi = volume processed at each plant  i  {1, 2, 3, 4, 5}. Here are the constraints that you are to use in your model: P1 + P2 + P3 + P4 + P5 = 100 Millions of gallons 19.2P1 + 19.6P2 + 19.8P3 + 19.2P4 + 18.2P5 = 1950.0 $k (94%)P1 + (95%)P2 + (97%)P3 + (94%)P4 + (90%)P5 = (95%)(P1 + P2 + P3 + P4 + P5) Purity level P1 = P4 Balance 1 P5 = P1 - 17.8 Balance 2 (10 pts) Start by converting the values along Column C into $k by using array functionality and the value in Cell D26, entering these values (to one decimal place; same as shown above) in the shaded cells along Column D. (5 pts per row) Next, fill in the [C] and [R] matrices for the above constraint equations. Report the third row as a percent to no decimal places. The below values MAY be typed in; all other values are to be performed via Excel: First row: (Row 31) 1 & 100 Fourth row: (Row 34) 1, -1, & 0 Fifth row: (Row 35) 1, -1, 0, & -17.8 (20 pts) Determine the S-matrix along column T; no formatting. Then answer the questions in the next text box.

1. (5 pts) You should have found that one of the plants has a solution that is almost 0 (if not, you erred); which plant has this result? Answer Here ith only a number  2. (10 pts) Use the ROUND macro in Column V to round the values in [S] to one decimal place (these values are[S2]). You are permitted to use an array process, and you are permitted to type in a 1 in the ROUND macro to define the number of decimal places to which you want to round. 3. (5 pts) Based on your answer to #1, take that plant "off line" by typing in a zero in first row of [C] underneath that plant's alphanumeric designation. 4. (20 pts) Then use the SUMPRODUCT macro and any other macros required to calculate the total cost in Cell V37; watch decimals. 5. (20 pts) Now appropriately calculate (via Excel) the final purity value in Cell V39. Watch your formatting. Remember, you must divide the SUMPRODUCT value by the total volume being processed, as defined in Cell P31; do NOT type in this value! SAVE!

EX2-2 70

(c)2017 Second Wind Productions, LLC

(c)2017 Second Wind Productions, LLC

A deep sea drone submersible is being tested, and a portion of its underwater path is depcted in the below graphic. '0' along the vertical axis represents sea level, whereas the remaining values along that axis are in coded (aka, classified) depth units. The horizontal axis represents equally-spaced time indices such that values prior to '0' represent a pre-test phase (the drone was launched from a submerged submarine). It is believed that the overall path can be modeled by a 'simple' 8th order polynomial function (at least, that's what the designers tell us). You are going to test this belief at the right, and then answer some questions below. (30 pts) Start by filling in [C] and [V]; see instructions along Row 4. (15 pts) Now, determine and format [S]; remember to shade it (not too dark, please!). (5 pts) What is the realized Order (integer value) of this polynomial? Answer Here  (15 pts) Based on your equation, what are the "zeroes" for this function. These would represent where the drone broke the surface of the sea. Report either as an integer, or to one decimal place. If the values cannot be determined, type in "No Solution." Answer(s) 

EX2-3 50

(c)2017 Second Wind Productions, LLC

(c)2017 Second Wind Productions, LLC

Consider the 4-distance mobile depicted at the right  Set up (by typing in) and solve for the four designated distances, d1-d4, immediately below this text box  Remember to lightly shade your matrices; report only [S] as fractions to 3 digits. 25 points for setting up the system, 25 points for the solution and formatting of same. I suggest that you set up the two systems on paper and sum the moments on each side before entering values on this worksheet.

EX2-4 80

(c)2017 Second Wind Productions, LLC

(c)2017 Second Wind Productions, LLC

A machine is in one of 5 possible states at any given instance: A = Producing without any problems B = Idle (not producing, but no problems) C = Down due to repairs that can be fixed in less than 2 hours D = Down due to repairs that can be fixed in 2 - 8 hours E = Down due to repairs that will take longer than 8 hours to fix The one-step transition matrix is shown at the above right . . . (15 pts) Start by finish filling in the one-step transition matrix by appropriately selecting the values along Column S and subtracting off the given values (same as we did on the HW). You MUST select the values in Column S! Do not lose all points on this worksheet by typing in values! (15 pts) Generate a three-step transition matrix (whichever MMULT method you would like to use), placing that matrix or those matrices) below the first (given) matrix. Make sure to identify in Column T when you have reached the three-step matrix (you may type in a '3'). Express the values as a percentage to one decimal place. (10 pts) Based on your 3-step transition matrix, given that the machine starts in State E, what is the probability that it will transition to State A in three steps? Respond Here  (10) Starting with your 3-step transition matrix, find the steady state probabilities, reporting these final values to 4 decimal places. (5 pts) In the long run, in which state is the machine most probably to be? Respond Here  (25 pts) Use the space below your steady state matrix to determine the following: It is assumed that if the machine is down for repairs it could otherwise be making product (that is, not otherwise 'idle'). Following are the expected costs associated with States C-E should the machine be in any of those states: C cost = $2,761 D cost = $7,350 Type in these values just below their respective columns just underneath your steady state matrix E cost = $22,862 Use SUMPRODUCT to determine the total expected cost for the machine to be down for repairs of some sort. Run this calculation just below your row of the given repair costs (). Report to the penny below what expected cost will be incurred in the long run due to the machine being down in need of repairs. Watch units and decimals! Respond Here 

The values along the main diagonal represent the probabilities of the machine staying in a given state. Use the values along Column S and the SUM macro to determine these values.

EX2-5 35

Here's the deal, here's a picture of (Pepper) Jack. Based on the relative dimensions (aspect) and orientation of this initial picture, you need to match each transformed picture below in Column E to its transformation matrix; you will do this by typing in the designated merged cells (along Column D) the letter associated with the correct transformation matrix. 5 points each (7 entries). Hungry Jack