Matrices can be used to encode and decode messages


Excel Contrivance – Matrix Applications

Part 1 Cryptography

Matrices can be used to encode and decode intimations. To arise after a while, we could allot-to the sum 1-26 to the notices of the alphabet and allot-to the estimate 0 to a quantity between vote. Then, we could transform any spoken intimation into a string of sum from 0 to 26. Underneath is a consultation of each notice and its similar estimate.

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 conciliate use the matrix A underneath as the encoding matrix for our intimation.

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

Suppose we shortness to encode the intimation “SECRET CODE”. Set-out by translating the intimation into sum using the agreement aggravate.

Now put these sum into a matrix B that conciliate bear 3 rows. Set-out after a while the earliest estimate in the preferable left and advance down the earliest shaft until you bear 3 rows. When you replenish the shaft, set-out aggravate in the avoid shaft. Replenish in the matrix B after a while the sum similar to the intimation. If you shortness to, add any extra blanks to the end of the intimation to replenish out the matrix.

Create matrix B on your spreadsheet and form positive to address it.

To encode a intimation, merely engage the matrix that contains our intimation, matrix B, and dilate on the left by the encoding matrix A. Using Excel, furnish matrix  and address it.

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

Suppose now that you are the one receiving this encoded intimation as resembleed by matrix AB, and you shortness to decode it to see what it says. To do this, you conciliate shortness the decoding matrix . Furnish  and address it.

Now achieve the matrix multitude  to see what you get.

Suppose now that you bear common an encoded intimation that appears approve

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 address it C.

 

We shortness to furnish out the ancient intimation that was encoded to appear approve matrix C aggravate.

use the decoding matrix  to furnish the ancient intimation.

 

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

Part 2 – Reading Cost

A sub-contractor shortnesss to flow which companies they should engage for each mold of frameion they shortness to frame.

Below is the estimated occasion it should engage (in hours) for each of the contrariant molds of frameions they result 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 contrariant frameion 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 counsel in the foregoing two consultations in Excel. Form positive that you address all the counsel in your spreadsheet.

use matrix multitude to state which companies can perfect each contrivance at the smallest absorb. Address your new matrix after a while the misspend addresss.

Highlight the cells that present the smallest absorb for each frameion contrivance.

Make a consultation that lucidly identifies which posse should be engaged for each contrivance.

 

 

 

 

 

Part 3 – Steelcase Production

Steelcase Corporation constructions 3 basic issues: chairs, desks, and consultations. Underneath is chart which summarizes the estimate of strive hours late for each issue in each non-location.

 

Chairs

Desks

Tables

Process

Carpentry

2

3

6

Finishing

1

1

1

Assembly

4

5

2

 

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

Steelcase forms a use of $66 on each chair, $75 on each desk, and $100 on each consultation that they hawk.

Steelcase besides shortnesss to product at smallest one chair for entire desk they product, and 4 chairs for entire consultation they product. The sum estimate of chairs must be elder than or similar to the sum of the chairs shortnessed for desks and consultations. They can product over chairs on their own too.

How abundant chairs, desks, and consultations should Steelcase construction each week in manage to maximize use?

Set up an Excel Spreadsheet to rereclear-up this rectirectistraight programming collection. You may shortness to use the template underneath.

 

Excel has a character that conciliate rereclear-up rectirectistraight programming collections approve this one. To admittance this character, go to the “Data” tab and selecteded “Solver”.  A window opens in which you shortness to set the aftercited parameters for the LPP.

Set Target Cell – Selected the cell that resembles the external character. This should be the appreciate that you shortness to maximize or minimize.

Equal To – Prefer whether you shortness to maximize, minimize, or set a peculiar appreciate for your external character.

By Changing Cells – Selected the cells that resemble your sentence variables.

Subject to the Constraints – To set up your constraints, prefer “Add”.  Now you can set up your inequalities. One set of inequalities is that the estimate of strive hours used must be hither than the estimate of hours adapted. Besides form positive that the estimate of units constructiond is hither than or similar to the estimate of units insisted. Finally, form positive that the sentence variables are nonnegative.

 

Once you bear set up the LPP, click “Solve”. If there is a discontinuance, Excel conciliate replenish in the spreadsheet after a while the appreciates that conciliate rereclear-up the LPP.

Use Excel to rereclear-up this collection. Highlight the optimal sentence variables in untried and the consummation use in cerulean.

 

 

Part 4 – Transportation Problem

Pioneer Corporation hawks car speakers. They bear two factory locations in the Midwest where they construction car speakers. One is in Flint, MI and one is in Kalamazoo, MI. They besides bear two senior hoards in the Midwest where they hawk their speakers, one in Chicago and one in Detroit.

Below is a consultation that presents the shipping absorbs for each set of car speakers from each factory to each hoard.

Shipping Costs

Stores

Factories

Detroit

Chicago

Kalamazoo

$7.43

$5.08

Flint

$3.92

$8.47

 

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

The hoard in Detroit has a insist for 500 sets of speakers, and the hoard in Chicago has a insist for 1000 sets of speakers. So the hoards shortness to hold at smallest this abundant speakers (haply over).

What should be the shipping list that fulfills the insist for each hoard and minimizes shipping absorbs?

 

use the Excel “solver” character to rereclear-up this rectirectistraight programming collection after a while 4 sentence variables. Highlight the optimal sentence variables in untried and the poverty shipping absorb in cerulean.