Date:
8.2(c) Notes: Matrix Application
Lesson Objective: Use matrix operations to
model and solve real-life problems
CCSS: N.VM.9
You will need: graphing calculator
Real-World App: What are the profits for each
outlet?
This is Jeopardy!!!: This is BA.
A = -1 -2
B=
-2
5
Lesson 1: Increased Production
A corporation has four factories, each of which
manufactures sport utility vehicles and pickup
trucks. The number of units of vehicle i produced at factory j in one day is represented by
aij in the matrix
100
90
70
30
A=
40
20
60
60
Find the production levels if production is
increased by 10%.
Lesson 1: Increased Production
Find the production levels if production is
increased by 10%.
A=
=
100
40
90
20
70
60
30
60
Lesson 2: Revenue
A manufacturer of electronics produces three
models of portable CD players, which are
shipped to two warehouses. The number of
units of model i that are shipped to warehouse j
is represented by aij in the matrix below. The
price per unit is given by bij below. Compute BA
and interpret the result.
5000 4000 B = [ $39.50 $44.50 $56.50 ]
A = 6000 10,000
8000 5000
Lesson 2: Revenue
A manufacturer of electronics produces three
models of portable CD players, which are
shipped to two warehouses. The number of
units of model i that are shipped to warehouse j
is represented by aij in the matrix below. The
price per unit is given by bij below. Compute BA
and interpret the result.
BA = [
][
]=[
]
5000 4000 B = [ $39.50 $44.50 $56.50 ]
A = 6000 10,000
]
8000 5000 BA = [
Lesson 3: Profits
A fruit grower raises 2 crops, which are shipped to
3 outlets. The list below shows how many units of
each crop are shipped to each outlet. The profit
per unit for Crop 1 is $3.75, and the profit per unit
for Crop 2 is $7.00. Find the profits for each outlet.
Outlet 1 Outlet 2 Outlet 3
Crop 1
Crop 2
100
125
75
150
75
100
Lesson 3: Profits
A fruit grower raises 2 crops, which are shipped to
3 outlets. The list below shows how many units of
each crop are shipped to each outlet. The profit
per unit for Crop 1 is $3.75, and the profit per unit
for Crop 2 is $7.00. Find the profits for each outlet.
A = [2 x 3]
Outlet 1 Outlet 2 Outlet 3
A=
Crop 1
Crop 2
100
125
75
150
75
100
Lesson 3: Profits
A fruit grower raises 2 crops, which are shipped to
3 outlets. The list below shows how many units of
each crop are shipped to each outlet. The profit
per unit for Crop 1 is $3.75, and the profit per unit
for Crop 2 is $7.00. Find the profits for each outlet.
A = [2 x 3]
C=
= [1 x 3] or [3 x 1]
Outlet 1 Outlet 2 Outlet 3
A=
Crop 1
Crop 2
100
125
75
150
75
100
Lesson 3: Profits
A fruit grower raises 2 crops, which are shipped to
3 outlets. The list below shows how many units of
each crop are shipped to each outlet. The profit
per unit for Crop 1 is $3.75, and the profit per unit
for Crop 2 is $7.00. Find the profits for each outlet.
A = [2 x 3] B = [
] C=
= [1 x 3] or [3 x 1]
Outlet 1 Outlet 2 Outlet 3
A=
Crop 1
Crop 2
100
125
75
150
75
100
Outlet 1
C=
Profit
Outlet 2
Outlet 3
Lesson 3: Profits
A fruit grower raises 2 crops, which are shipped to
3 outlets. The list below shows how many units of
each crop are shipped to each outlet. The profit
per unit for Crop 1 is $3.75, and the profit per unit
for Crop 2 is $7.00. Find the profits for each outlet.
A = [2 x 3] B = [1 x 2] C =
= [1 x 3] or [3 x 1]
Outlet 1 Outlet 2 Outlet 3
A=
Crop 1
Crop 2
B=
100
125
Crop 1 Crop 2
Profit
3.75
7
75
150
75
100
Outlet 1
C=
Profit
Outlet 2
Outlet 3
Lesson 3: Profits
A fruit grower raises 2 crops, which are shipped to
3 outlets. The list below shows how many units of
each crop are shipped to each outlet. The profit
per unit for Crop 1 is $3.75, and the profit per unit
for Crop 2 is $7.00. Find the profits for each outlet.
A = [2 x 3] B = [1 x 2] C = BA = [1 x 3] or [3 x 1]
Outlet 1 Outlet 2 Outlet 3
A=
Crop 1
Crop 2
B=
100
125
Crop 1 Crop 2
Profit
3.75
7
75
150
75
100
Outlet 1
C=
Profit
Outlet 2
Outlet 3
Lesson 3: Profits
A = [2 x 3] B = [1 x 2] C = BA = [1 x 3] or [3 x 1]
Outlet 1 Outlet 2 Outlet 3
A=
Crop 1
Crop 2
B=
BA =
100
125
Crop 1 Crop 2
Profit
3.75
7
75
150
75
100
Outlet 1
C=
Profit
Outlet 2
Outlet 3
8.2(c): Do I Get It? Yes or No
Two softball teams submit equipment lists to
their sponsors.
Each bat costs $80, each ball costs $6, and each
glove costs $60. Use matrices to find the total
cost of equipment for each team.
Lesson 1: (1 x n) ∙ (n x 1) Multiplication Recap
B.
Find AB and BA.
AB =
=
Lesson 1: (1 x n) ∙ (n x 1) Multiplication Recap
B.
1∙
2∙
BA =
3∙
4∙
1∙
2∙
3∙
4∙
1∙
2∙
3∙
4∙
1∙
2∙
3∙
4∙
=