This document provides instructions for four Excel projects involving matrices and linear programming: 1) Using matrices to encode and decode messages by assigning numbers to letters. 2) Using matrix multiplication to determine the lowest cost construction companies for different building projects. 3) Setting up a linear program to maximize profits by determining the optimal number of chairs, desks, and tables to produce. 4) Setting up a transportation problem to minimize shipping costs by determining the optimal shipping schedule between factories and stores.

1. Excel Project – Matrix Applications
Part 1 – Cryptography
Matrices can be used to encode and decode messages. To begin
with, we could assign the numbers 1-26 to the letters of the
alphabet and assign the number 0 to a space between words.
Then, we could translate any verbal message into a string of
numbers from 0 to 26. Below is a table of each letter and its
corresponding number.
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

2. 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 will use the matrix A below as the encoding matrix for our
message.

3. Enter the encoding matrix A in your spreadsheet and label it.
Suppose we want to encode the message “SECRET CODE”.
Start by translating the message into numbers using the
correspondence above.
Now put these numbers into a matrix B that will have 3 rows.
Start with the first number in the upper left and move down the
first column until you have 3 rows. When you fill the column,
start over in the second column. Fill in the matrix B with the
numbers corresponding to the message. If you need to, add any
extra blanks to the end of the message to fill out the matrix.
Create matrix B on your spreadsheet and make sure to label it.
To encode a message, simply take the matrix that contains our
message, matrix B, and multiply on the left by the encoding
matrix A. Using Excel, find matrix and label it.
Now our message “SECRET CODE” has been encoded and is
represented by the numbers in matrix AB.
Suppose now that you are the one receiving this encoded
message as represented by matrix AB, and you want to decode it
to see what it says. To do this, you will need the decoding
matrix . Find and label it.
Now perform the matrix multiplication to see what you get.
Suppose now that you have received an encoded message that
looks like
52
28
28

4. 25
27
35
22
89
47
36
50
41
50
37
110
46
68
35
71
75
36
Enter this matrix in Excel and label it C.
We want to find out the original message that was encoded to
look like matrix C above.
Use the decoding matrix to find the original message.
Use the table at the top to decode the message and write the
message in your Excel spreadsheet.
Part 2 – Construction Cost
A sub-contractor needs to decide which companies they should

5. hire for each type of building they want to construct.
Below is the estimated time it should take (in hours) for each of
the different types of buildings they work 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 different construction
companies in the area.

6. 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 information in the previous two tables in Excel. Make
sure that you label all the information in your spreadsheet.
Use matrix multiplication to determine which companies can

7. complete each project at the lowest cost. Label your new matrix
with the appropriate labels.
Highlight the cells that give the lowest cost for each building
project.
Make a table that clearly identifies which company should be
hired for each project.
Part 3 – Steelcase Production
Steelcase Corporation manufactures 3 basic products: chairs,
desks, and tables. Below is chart which summarizes the number
of labor hours spent for each product in each division.
Chairs
Desks
Tables
Process
Carpentry
2
3
6
Finishing
1
1
1
Assembly
4
5

8. 2
In a given week, Steelcase has 250 hours available for
carpentry, 100 hours available for finishing, and 400 hours
available for assembly.
Steelcase makes a profit of $66 on each chair, $75 on each desk,
and $100 on each table that they sell.
Steelcase also needs to produce at least one chair for every desk
they produce, and 4 chairs for every table they produce. The
total number of chairs must be greater than or equal to the sum
of the chairs needed for desks and tables. They can produce
more chairs on their own too.
How many chairs, desks, and tables should Steelcase
manufacture each week in order to maximize profit?
Set up an Excel Spreadsheet to solve this linear programming
problem. You may want to use the template below.
Chairs
Desks
Tables
Total
Carpentry
Finishing

9. Assembly
Chairs Needed
Profit Per Unit
Total Profit
Subtotal

10. Excel has a function that will solve linear programming
problems like this one. To access this function, go to the “Data”
tab and select “Solver”. A window opens in which you need to
set the following parameters for the LPP.
Set Target Cell – Select the cell that represents the objective
function. This should be the value that you want to maximize or
minimize. Do not hard code (enter a specific number into) this
cell.
Equal To – Choose whether you want to maximize, minimize, or
set a specific value for your objective function.
By Changing Cells – Select the cells that represent your
decision variables. Do not hard code (enter specific numbers
into) these cells.
Subject to the Constraints – To set up your constraints, choose
“Add”. Now you can set up your inequalities. One set of
inequalities is that the number of labor hours used must be less
than the number of hours available. Also make sure that the
number of units manufactured is less than or equal to the
number of units demanded. Finally, make sure that the decision
variables are nonnegative.
Once you have set up the LPP, click “Solve”. If there is a
solution, Excel will fill in the spreadsheet with the values that
will solve the LPP.
Use Excel to solve this problem. Highlight the optimal decision
variables in green and the maximum profit in blue.

11. Part 4 – Transportation Problem
Pioneer Corporation sells car speakers. They have two factory
locations in the Midwest where they manufacture car speakers.
One is in Flint, MI and one is in Kalamazoo, MI. They also have
two major stores in the Midwest where they sell their speakers,
one in Chicago and one in Detroit.
Below is a table that gives the shipping costs for each set of car
speakers from each factory to each store.
Shipping Costs
Stores
Factories
Detroit
Chicago
Kalamazoo
$7.43
$5.08
Flint
$3.92
$8.47
The factory in Kalamazoo has a supply of 700 sets of speakers,
and the factory in Flint has a supply of 900 sets of speakers. So
the factories cannot ship more than they currently have.
The store in Detroit has a demand for 500 sets of speakers, and
the store in Chicago has a demand for 1000 sets of speakers. So
the stores need to receive at least this many speakers (possibly
more).
What should be the shipping schedule that fulfills the demand
for each store and minimizes shipping costs?
Set up a spreadsheet to solve this problem. You may use the
template provided below.
Speakers
Detroit

12. Chicago
Sent
Kalamazoo
Flint
Received
Shipping Costs
Detroit
Chicago
Kalamazoo
Flint
Total Cost

13. Use the Excel “solver” function to solve this linear
programming problem with 4 decision variables. Highlight the
optimal decision variables in green and the minimum shipping
cost in blue. Do not hard code the target or changing cells (do
not enter specific numbers into those cells).