Matrices can be used to encode and decode messages


Excel Purpose – Matrix Applications

Part 1 Cryptography

Matrices can be used to encode and decode intimations. To arise after a while, we could advance the aggregate 1-26 to the scholarship of the alphabet and advance the enumerate 0 to a meafast among opinion. Then, we could render any oral intimation into a string of aggregate from 0 to 26. Adown is a consideration of each communication and its identical enumerate.

Blank

A

B

C

D

E

F

G

H

I

J

K

L

M

0

1

2

3

4

5

6

7

8

9

10

11

12

13

 

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

14

15

16

17

18

19

20

21

22

23

24

25

26

 

We accomplish use the matrix A adown as the encoding matrix for our intimation.

Enter the encoding matrix A in your spreadsheet and designate it.

Suppose we lack to encode the intimation “SECRET CODE”. Initiate by translating the intimation into aggregate using the writing balancehead.

Now put these aggregate into a matrix B that accomplish possess 3 rows. Initiate after a while the principal enumerate in the loftier left and actuate down the principal shaft until you possess 3 rows. When you gorge the shaft, initiate balance in the promote shaft. Gorge in the matrix B after a while the aggregate identical to the intimation. If you deficiency to, add any extra blanks to the end of the intimation to gorge out the matrix.

Create matrix B on your spreadsheet and fashion fast to designate it.

To encode a intimation, singly procure the matrix that contains our intimation, matrix B, and extend on the left by the encoding matrix A. Using Excel, confront matrix  and designate it.

Now our intimation “SECRET CODE” has been encoded and is embodyed by the aggregate in matrix AB.

Suppose now that you are the one receiving this encoded intimation as embodyed by matrix AB, and you lack to decode it to see what it says. To do this, you accomplish deficiency the decoding matrix . Confront  and designate it.

Now execute the matrix reiter-ation  to see what you get.

Suppose now that you possess common an encoded intimation that faces enjoy

52

28

28

25

27

35

22

 

 

89

47

36

50

41

50

37

 

 

110

46

68

35

71

75

36

 

 

 

Enter this matrix in Excel and designate it C.

 

We lack to confront out the primary intimation that was encoded to face enjoy matrix C balancehead.

use the decoding matrix  to confront the primary intimation.

 

use the consideration at the top to decode the intimation and transcribe the intimation in your Excel spreadsheet.

Part 2 – Explanation Cost

A sub-contractor deficiencys to flow which companies they should employ for each image of edifice they lack to invent.

Below is the estimated spell it should procure (in hours) for each of the unanalogous images of edifices they toil on.

Building

Excavating

Framing

Electrical

Plumbing

Finishing

Office Space

45

100

88

32

312

School

56

250

47

28

270

Apartments

84

480

75

25

244

Grocery Store

95

160

26

78

236

Below are the hourly rates for some unanalogous invention companies in the area.

Company

Bouma

Pinnacle

Rockford

McGraw

Excavating

$350

$300

$285

$245

Framing

$225

$275

$280

$280

Electrical

$405

$375

$295

$350

Plumbing

$150

$240

$225

$200

Finishing

$250

$190

$260

$215

 

Input the knowledge in the earlier two considerations in Excel. Fashion fast that you designate all the knowledge in your spreadsheet.

use matrix reiter-ation to mention which companies can thorough each purpose at the smallest absorb. Designate your new matrix after a while the misapply designates.

Highlight the cells that grant the smallest absorb for each edifice purpose.

Make a consideration that plainly identifies which sodality should be employd for each purpose.

 

 

 

 

 

Part 3 – Steelcase Production

Steelcase Corporation moldings 3 basic consequences: chairs, desks, and considerations. Adown is chart which summarizes the enumerate of drudge hours elapsed for each consequence in each disunion.

 

Chairs

Desks

Tables

Process

Carpentry

2

3

6

Finishing

1

1

1

Assembly

4

5

2

 

In a grantn week, Steelcase has 250 hours adapted for carpentry, 100 hours adapted for finishing, and 400 hours adapted for parterre.

Steelcase fashions a avail of $66 on each chair, $75 on each desk, and $100 on each consideration that they vend.

Steelcase besides deficiencys to effect at last one chair for aggregate desk they effect, and 4 chairs for aggregate consideration they effect. The aggregate enumerate of chairs must be main than or similar to the sum of the chairs deficiencyed for desks and considerations. They can effect over chairs on their own too.

How frequent chairs, desks, and considerations should Steelcase molding each week in arrange to maximize avail?

Set up an Excel Spreadsheet to work-out this direct programming height. You may lack to use the template adown.

 

Excel has a discharge that accomplish work-out direct programming heights enjoy this one. To path this discharge, go to the “Data” tab and selecteded “Solver”.  A window opens in which you deficiency to set the subjoined parameters for the LPP.

Set Target Cell – Selected the cell that embodys the external discharge. This should be the appraise that you lack to maximize or minimize.

Equal To – Select whether you lack to maximize, minimize, or set a peculiar appraise for your external discharge.

By Changing Cells – Selected the cells that embody your judgment variables.

Subject to the Constraints – To set up your constraints, select “Add”.  Now you can set up your inequalities. One set of inequalities is that the enumerate of drudge hours used must be near than the enumerate of hours adapted. Besides fashion fast that the enumerate of units moldingd is near than or similar to the enumerate of units ask-fored. Finally, fashion fast that the judgment variables are nonnegative.

 

Once you possess set up the LPP, click “Solve”. If there is a explanation, Excel accomplish gorge in the spreadsheet after a while the appraises that accomplish work-out the LPP.

Use Excel to work-out this height. Highlight the optimal judgment variables in uncooked and the completion avail in bluish.

 

 

Part 4 – Transportation Problem

Pioneer Corporation vends car speakers. They possess two factory locations in the Midwest where they molding car speakers. One is in Flint, MI and one is in Kalamazoo, MI. They besides possess two important treasures in the Midwest where they vend their speakers, one in Chicago and one in Detroit.

Below is a consideration that grants the shipping absorbs for each set of car speakers from each factory to each treasure.

Shipping Costs

Stores

Factories

Detroit

Chicago

Kalamazoo

$7.43

$5.08

Flint

$3.92

$8.47

 

The factory in Kalamazoo has a afford of 700 sets of speakers, and the factory in Flint has a afford of 900 sets of speakers. So the factories cannot ship over than they currently possess.

The treasure in Detroit has a ask-for for 500 sets of speakers, and the treasure in Chicago has a ask-for for 1000 sets of speakers. So the treasures deficiency to assent-to at last this frequent speakers (haply over).

What should be the shipping list that fulfills the ask-for for each treasure and minimizes shipping absorbs?

 

use the Excel “solver” discharge to work-out this direct programming height after a while 4 judgment variables. Highlight the optimal judgment variables in uncooked and the incompleteness shipping absorb in bluish.