1
AB103 – Statistical and Quantitative Methods
Solutions - Tutorial 5
Chapter 2 (ASWM)
2.1 (page 70)
2.21 (page 73)
a. Let
F
=
number of tons of fuel additive
S
=
number of tons of solvent base
Ma
x
40
F
+
30
S
s.t.
2/5
F
+
1
/
2
S
≤
200
Material 1
1
/
5
S
≤
5
Material
2
3
/
5
F
+
3
/
10
S
≤
21
Material
3
F
,
S
≥
0

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2
b.
.
0
10
20
30
40
50
10
20
30
40
50
60
70
Feasible
Region
Tons of Fuel Additive
Material 2
Optimal Solution
(25,20)
Material 3
Material 1
Tons of Solvent Base
c.
Material 2: 4 tons are used, 1 ton is unused.
d. No redundant constraints.
2.25 (pages 74-75)
S
F

3
Internet fund $20,000
Blue Chip fund $30,000
Annual return $ 5,100
b. The third constraint for the aggressive investor becomes
6
I
+ 4
B
≤
320
This constraint is redundant
; the available funds and the maximum Internet fund
investment constraints define the feasible region. The optimal solution is:
Internet fund $35,000
Blue Chip fund $15,000
Annual return $ 5,550
The aggressive investor places as much funds as possible in the high return but high risk
Internet fund.

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