MATH 1302  PRACTICE THIRD MIDTERM EXAM SOLUTIONS
WINTER 2008
1. Suppose an economy consists of three sectors – manufacturing, agriculture and services –
with unit consumptions as given in the following table.
Purchased
Inputs Consumed per Unit of Output
From:
Manufacturing
Agriculture
Services
Manufacturing
.20
.20
0
Agriculture
.30
.10
.30
Services
.10
0
.20
What production levels are needed to satisfy a final demand of 40 units from manufac
turing, 60 units from agriculture, and 80 units from services?
Answer:
We have
C
=
.
2
.
2
0
.
3
.
1
.
3
.
1
0
.
2
,
I

C
=
.
8

2
.
0

.
3
.
9

.
3

.
1
0
.
8
,
d
=
40
60
80
.
We row reduce
£
I

C
d
/
to get
.
8

.
2
0
40

.
3
.
9

.
3
60

.
1
0
.
8
80
∼
1
0
0
82
.
8
0
1
0
131
.
0
0
0
1
110
.
3
.
Therefore, to meet the given demand, manufacturing needs to produce 82.8 units, agriculture
needs to produce 131.0 units and services needs to produce 110.3 units.
2. Suppose that
z
=

1 + 4
i,
w
= 2

2
i.
Perform the following operations, writing your answers in the form
a
+
bi
where
a, b
∈
R
.
a)

z

Solution:

z

=
p
(

1)
2
+ 4
2
=
√
17.
b) ¯
w
Solution:
¯
w
= 2 + 2
i
.
c)
w/z
Solution:
w
z
=
2

2
i

1 + 4
i
·

1

4
i

1

4
i
=

10

6
i
17
=

10
17

6
17
i.
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MAT 1302  PRACTICE THIRD MIDTERM EXAM SOLUTIONS
d)
wz
Solution:
wz
= (2

2
i
)(

1 + 4
i
) = 6 + 10
i
e) 3
z
+ 2
w
Solution:
3
z
+ 2
w
= 1 + 8
i
3. If
A
=
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 Fall '09
 MarianKupczynski
 Math, 2W, Midterm Exam Solutions, Chess opening, Howard Staunton, 10 6 W, Manufacturing Agriculture Services Manufacturing

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