Honors Discrete DMTA MATRIX QUIZ REVIEW GUIDE - SOLUTIONS
1. A group of students is planning a retreat. They have contacted three lodges in the vicinity to inquire
about rates. They found that Crystal Lodge charges $13.00 per person per day for lodging, $20.00 per
day for food, and $5.00 per person for use of the recreational facilities. Springs Lodge charges $12.50 for
lodging, $7.50 for use of the recreational facilities, and $19.50 for
Lodging Food Rec
meals. Bear Lodge charges $18.00 a day for meals, $20.00 per night
Crystal  13
20
5 
for lodging, and there is no extra charge for the recreational facilities.

Springs 12.50 19.50 7.50
Display this information in a matrix C where the rows are the lodges.
Label the rows and columns.
Bear
18
0 
 20
2. Your math club is planning a Saturday practice session for an upcoming math contest. For lunch the
students ordered 35 Mexican lunches, 6 bags of corn chips, 6 containers of salsa, and 12 six-packs of cold
drinks. Suppose that the club pays $4.50 per lunch, $1.97 per bag of corn chips, $2.10 for each container
of salsa, and $2.89 for each six-pack of cold drinks.
$4.50 L
35 6 6 12 $1.97 CC
2a. Set up a matrix multiplication to find the total cost.
L CC S D $2.10 S  $216.60
Identify the rows and columns of your matrices.


$2.89 D
2b. Find the total cost.
Quantity
Pr ice
3. Mr. Jones has been shopping for a vacuum-powered cleaning system. He found one at Z-Mart and
another model at Base Hardware. The Z-Mart system cost $39.50, disposal cartridges were 6 for $24.50,
and storage cases were $8.50 each. At Base Hardware the system cost $49.90, cartridges were 6 for
$29.95, and cases were $12.50 each.
S DC SC
3a. Write and label a matrix showing the prices for the three items
Z  Mart  39.50 24.50 8.50 
at the two stores.
49.90 29.95 12.50
Base


3b. Mr. Jones decided to wait and see if the prices for the systems
 35.55 22.05 7.65
would be reduced during the upcoming sales. When he went back during
 39.92 23.96 10 
the sales, the Z-Mart prices were reduced by 10% and the Base Hardware


prices were reduced by 20%. Construct a matrix showing the sale prices for
each of the three items at the two stores.
 3.95 2.45 0.85
3c. Use matrix subtraction to compute how much Mr. Jones could save for
9.98 5.99 2.50
each item at the two stores.


4. An artist creates plates and bowls from small pieces of colored woods. Each plate requires 100 pieces of
ebony, 800 pieces of walnut, 600 pieces of rosewood, and 400 pieces of maple. It takes 200 ebony pieces,
1200 walnut pieces, 1000 rosewood pieces, and 800 pieces of maple to make a large bowl. A small bowl
takes 50 pieces of ebony, 500 walnut pieces, 450 rosewood pieces, and 400 pieces of maple.
4a. She currently has orders for five plates, three large
Ebony Walnut Rose Maple
bowls, and seven small bowls. Set up and solve a
P
100 800 600 400
matrix multiplication to compute the number of pieces P LB SB
 200 1200 1000 800
5 3 7 LB
of each type of wood needed for the order.


 50 500 450 400
SB
4b. Next week she has one order for 6 plates, 2 large
 1450 11,100 9150 7200
bowls, and 4 small bowls to ship out of town, and a
Ebony Walnut Rose Maple
P LB SB P
second order for 12 plates and 9 small bowls for a
100 800 600 400
local market. Set up and solve a matrix multiplication  6 2 7
 200 1200 1000 800
12 0 9 LB
to compute the number of pieces of each type of




 50 500 450 400
SB
wood needed to complete each order separately.
7400 5600
1200 9200


1650 14,100 11,250 8400
5. Four local restaurants offer all soups and sandwiches for a lunch
special given in the table. On Monday, you order 5 soups and 4
sandwiches. On Wednesday, you order 2 soups and 7 sandwiches.
On Friday, you order 6 soups and 10 sandwiches.
5a. Set up and solve a matrix multiplication to find the cost from
each restaurant per day of the week.
Restaurant #1
Restaurant #2
Restaurant #3
Restaurant #4
Soup
$2.75
$3.15
$2.90
$2.50
Sandwich
$7.20
$6.75
$7.00
$7.50
M W F
42.55 55.90 88.50
42.75 53.55 86.40


42.50 54.80 87.40


42.50 57.50 90.00
R#1 R#2 R #3 R#4
M 5 4   2.75 3.15 2.90 2.50
M 42.55 42.75 42.50 42.50
W  2 7  7.20 6.75 7.00 7.50 
W 55.90 53.55 54.80 57.50
F 6 10 R #1 R#2 R #3 R#4
F 88.50 86.40 87.40
90 
Option 2:
R #1  2.75
R #2  3.15
R #3  2.90

Option 1: R #4  2.50
7.20
5 2 6  R #1
6.75 
4 7 10  R #2

7.00
 M W F R#3
7.50
R #4
5b. Which restaurant has the best deal per day of the week?
MONDAY = R#3 + R#4
WEDNESDAY and FRIDAY = R#2
5c. If you can only order from one of four restaurants for the entire week, which restaurant should you
choose? R#2 overall best
6. Three music classes at Central High are selling candy as a fundraiser. The number of each kind of
candy sold by each of the three classes is shown in the following table.
The profit for each type of candy is
Jazz Band Symphonic Band Orchestra
sour balls, 30 cents; chocolate chews,
Almond Bars
300
220
250
50 cents; almond bars, 25 cents; and
Chocolate Chews
240
330
400
mint patties, 35 cents. Use matrix
Mint
Patties
150
200
180
multiplication to compute the profit
Sour balls
175
150
160
made by each class on its candy sales.
 300
.25 .50 .35 .30 240
AB CC MP SB 150

175
220 250
$300 $335 $373.5
330 400

200 180  Jazz Symphonic Orchestra

150 160 
7. The students at Central High are planning to hire a band for the prom. Their choices are A, B, and C.
They survey the Sophomore, Junior, and Senior
The student population by class and sex is:
Male Female
classes and find the following percentages of
10
th
 235 225
students prefer the bands,
 205 215
11th
10th 11th 12th


12th
A  20% 35% 40%
175 190 
B  30% 30% 25%
C 50% 35% 35%
Use matrix multiplication to find:
7a. number of males and females who prefer each band. 7b. total number of students who prefer each band.
( 3  3)
.20 .35 .40
.30 .30 .25


.50 .35 .35
( 3  2)
( 3  2)
 235 225 188.75 196.25 
 205 215  175.75 179.5 

 

175 190   250.5 254.25
A  188.75 
196.25  385
B  175.75  179.5  355.25
C  250.5  254.25  504.75
8. The characteristics of a female reptile are shown in the following table. Suppose the initial female
population for the heard is given by P0  18 24 30 22 12 10
8a. What is the expected lifespan of this reptile?
Age Groups
Birth Rate Survival
(yrs)
Rate
30 YEARS
0
–
5
0
0.4
8b. Construct the Leslie matrix for this population.
5 – 10
0.6
0.7
0
0
0
 0 0. 4 0
10 – 15
1.2
0.8
0.6 0 0.7 0

15 – 20
1.3
0.9
0
0

20 – 25
0.4
0.6
1.2 0
0 0. 8 0
0
25 – 30
0
0
L


1.3
0.4

 0
0
0
0
0. 9
0
0
0
0
0
0
0
0


0
0.6

0 
8c. Find the new population distribution after 15 years? (Hint: How many cycles or transitions?)
15/5 = 3 transitions
P3  P0 L3  52.272 25.44 23464 4.032 12.096 12.96
8d. What is the total population of P6? TOTAL
= 129
P6  P0 L  55.682 23.908 14.980 11.709 12.822 10.136
6
9. The characteristics of an insect are shown in the following table. Suppose the initial female population
for the heard is given by P0  24 30 36 20 10
9a. What is the expected lifespan of this insect?
Age Groups
Birth
Survival
(months)
Rate
Rate
20 MONTHS
9b. How long is a cycle or transition for this insect?
0–4
0
0.8
4–8
0.7
0.5
4 months long
9c. Construct the Leslie matrix for this population.
8 – 12
0.9
0.6
12 – 16
1.2
0.7
 0 .8 0 0 0 
16 – 20
0.3
0

 .7

L   .9

1.2
 .3
0
.5
0
0
0
0
0
0

0 
.6 0 

0 .7 
0 0 
0
9d. What is the total population of P9?
P9  P0 L9  110.933 80.694 37.85 20.246 14.036
TOTAL = 264

9e. Find the approximate number of female insects between 8 – 12 months in 5 transitions from now?
P5  P0 L5  #
#
27.6
#
#
