Bell Work
You are the head supervisor at the Shoe Department in
Cleveland, Ohio. As tax season has arrived, you are trying
to examine the commission amount for each salesman for
this month to file your taxes accurately. Here is what we
know…
▫ Leigh sold $5,200 in men’s shoes, $4,200 in women’s shoes,
and $2,300 in children’s shoes.
▫ Khalid sold $8,100 in men’s shoes, $8,400 in women’s shoes,
and $3,100 in children’s shoes.
▫ Ari sold $2,700 in men’s shoes, $7,400 in women’s shoes,
and $630 in children’s shoes.
▫ This month’s commission rate is 9.5% for men’s sales, 10%
for women’s sales, and 12% for children’s sales.
How do we begin to solve this problem?
Step One: Organize Data
Commission
Rate
Men’s Sales
9.5%
Leigh
Sales
Sales in
Sales in
Sales in
Men’s
Women’s Children’
Shoes
Shoes
s Shoes
$5,200
$4,200
$2,300
Khalid
$8,100
$8,400
$3,100
Women’s
Sales
10%
Ari
$2,700
$7,400
$630
Children’s
Sales
12%
Name
Step Two: Create Matrices
5200 4200 2300 


A  8100 8400 3100 
 2700 7400 630 
Dimensions?
9.5% 


B  10% 
12% 
Step Three: Multiply Matrices
1190.00 
A  B  1981.55 
1072.10 
Step Four: Analyze Results
What does each number represent in our matrix product?
Who earned the most in commissions? How do you know?
Who earned the least?
Let’s Try Another Problem!
Students collected recyclables for fund-raising over a 3-week period. Use
what you know about matrix operations to find the total amount of money
collected for each type of item.
Here’s what we know about the quantity of each item recycled…
▫ On week 1, students collected 29 pounds of glass. On week 2,
students collected 25 pounds of glass. On week 3, students
collected 16 pounds of glass.
▫ On week 1, students collected 8 pounds of cans. On week 2,
students collected 11 pounds of cans. On week 3, students
collected 6 pounds of cans.
▫ On week 1, students collected 163 pounds of newspapers. On
week 2, students collected 127 pounds of newspapers. On
week 3, students collected 206 pounds of newspapers.
▫ On week 1, students collected 53 pounds of office paper. On
week 2, students collected 107 pounds of office paper. On
week 3, students collected 84 pounds of office paper.
Here’s what we know about the earnings…
▫ During the first week, students earned $0.02 per
pound for glass, $0.70 per pound for cans, $0.02
per pound for newspaper, and $1.06 per pound for
office paper.
▫ During the second week, students earned $0.02
per pound for glass, $0.55 per pound for cans,
$0.01 per pound for newspaper, and $1.00 per
pound for office paper.
▫ During the third week, students earned $0.01 per
pound for glass, $0.42 per pound for cans, $0.02
per pound for newspaper, and $1.03 per pound for
office paper.
Step One: Organize Data
Recyclables Collected (pound)
Item
Wk 1
Wk 2
Wk 3
Price Per Pound ($)
Glass
29
25
16
Cans
8
11
6
News.
163
127
Office
Paper
53
107
Wk
Glass Cans News.
Office
Paper
206
1
0.02
0.70 0.02
1.06
84
2
0.02
0.55 0.01
1.00
3
0.01
0.42 0.02
1.03
Step Two: Create Two Matrices
 29
8
A
163

53
25
11
127
107
16 
0.02
0.70
0.02
1.06



6 


B  0.02 0.55 0.01 1.00 
206
0.01 0.42 0.02 1.03 

84 
Step Three: Multiply Matrices
1.24
0.44
A B  
7.86

 4.04
40.77
14.17
270.47
131.23
1.15
0.39
8.65
3.81
72.22 

25.66 
511.96 

249.70
Step Four: Analyze Results
Homework!
Which values matter in this matrix product?
How come the other values don’t matter?
How much did we earn from glass? Cans? Newspapers?
Office Paper?
How much did the students earn total?