f(x) = 5⋅x1 –
3⋅x1 +
2⋅x1 –
∀ xj ≥ 0
f(x) = 6⋅x1
x1
3⋅x1
x1
∀ xj ≥ 0
f(x) =
∀ xj≥ 0
x2
x2
x2
5⋅x2
№1
+ x3
a max
+ x3 + x4 + x5 = 5
+ 3⋅x3
= 4
+ 6⋅x3 + x4
= 11
+ x2 –
+ 2⋅x2 +
– x2 –
+ 3⋅x2 +
№2
x3 – 2⋅x4
a max
x3 + 6⋅x4 + x5 = 4
x3 + x 4
= 1
= 9
5⋅x3
6⋅x2 + x3 –
3⋅x1 – x2 + x3 +
+ 5⋅x3 +
x1
x1 + 2⋅x2 + 3⋅x3 +
f(x) = 7⋅x1 + x2 +
5⋅x1 + x2 +
– 2⋅x2 +
x1 – 3⋅x2 +
∀ xj ≥ 0
№3
x4
a max
6⋅x4 + x5 = 6
x4 – 7⋅x5 = 6
x4 + x5 = 6
№4
x3 – x4
a max
x3 + 3⋅x4 + x5 = 5
4⋅x3 + x4 + x5 = 3
= 2
5⋅x3
f(x) = 8⋅x1 + x2 – 3⋅x3
– x1 + x2 + x3
+ x3
2⋅x1
– x3
3⋅x1
∀ xj ≥ 0
№5
a max
+ 2⋅x4 + x5 = 4
– 3⋅x4 + 5⋅x5 = 3
+ 6⋅x4 + x5 = 6
№6
f(x) =
x2 – 3⋅x3 – x4 – x5 a max
= 2
–2⋅x1 – x2 + 2⋅x3
x1 + x2 + 4⋅x3 + x4 + 3⋅x5 = 8
+ 6⋅x5 = 5
3⋅x1 + x2 – x3
∀ xj ≥ 0
№7
f(x) =
∀ xj≥ 0
f(x) =
∀ xj ≥ 0
x1 – 2⋅x2 – x3 – x4
a max
+
x
–
x
+
x
2⋅x1
3
4
5 = 2
4⋅x1 + x2 + 3⋅x3 + x4 + 2⋅x5 = 7
+ x3 + 2⋅x4 + x5 = 2
– x1
x2 – 6⋅x3 + x4
6⋅x1 + x2 + x3 + 2⋅x4
– x3 + 7⋅x4
– x1
+ 2⋅x3 + x4
x1
№8
– 3⋅x5 a max
+ x5 = 9
+ 8⋅x5 =14
+ x5 = 3
№9
f(x) = –8⋅x1 – x2 – x3 + x4
a max
+
x
+
x
+
–2⋅x1
3⋅x3
4
5 = 5
3⋅x1 + x2 + x3 + 6⋅x4 + 2⋅x5 = 9
+ 2⋅x3 – x4 + 2⋅x5 = 3
– x1
∀ xj≥ 0
f(x) = – x1 + 3⋅x2 – x3 + x4
+ 3⋅x3 + x4
2⋅x1
– x3 + 2⋅x4 + 3⋅x5
x1
3⋅x1 + 3⋅x2 + 6⋅x3 + 3⋅x4 + 6⋅x5
∀ xj≥ 0
f(x) =
∀ xj≥ 0
№ 10
a max
= 4
= 4
=15
x4 – 3⋅x5
2⋅x2
x3
+
x5
4⋅x1 + x2 +
x3
+ 3⋅x5
– x1 + 3⋅x2 –
8⋅x1 + 4⋅x2 + 12⋅x3 + 4⋅x4 + 12⋅x5
f(x) = 10⋅x1 + 5⋅x2
8⋅x1 + 16⋅x2
2⋅x2
3⋅x2
∀ xj≥ 0
+
№ 11
a max
= 6
= 1
=24
№ 12
– 25⋅x3 + 5⋅x4
a max
+ 8⋅x3 + 8⋅x4 + 24⋅x5 =32
–
x3 + x4 +
x5 = 1
+ 2⋅x3 – x4 +
x5 =15
№ 13
– x3 + x4 + 2⋅x5 a max
f(x) = 6⋅x1
4⋅x1 + x2 + x3 + 2⋅x4 + x5 = 8
+ x4
= 2
2⋅x1 – x2
∀ xj ≥ 0
x1 + x2
+
f(x) = –5⋅x1 – x2 + 3⋅x3 – x4
x1 + 2⋅x2 + 3⋅x3 + 4⋅x4
3⋅x2 – x3 + 4⋅x4
+ 8⋅x4
4⋅x2
∀ xj≥ 0
f(x) = 5⋅x1
3⋅x1
3⋅x1
x1
∀ xj ≥ 0
+
+
+
–
3⋅x2 + 2⋅x3 –
4⋅x2 + x3
2⋅x2 + x3 +
3⋅x2
f(x) = 7⋅x1
+
x1 – x2 +
2⋅x1 + 2⋅x2 +
2⋅x1 + x2
∀ xj ≥ 0
f(x) = 6⋅x1
– x1
5⋅x1
3⋅x1
∀ xj ≥ 0
f(x) =
∀ xj ≥ 0
x3 –
x3
x3 +
x5 = 2
№ 14
a max
+ x5 = 7
= 7
+ x5 =12
№ 15
x4 + x5 a max
= 12
x4 + x5 = 16
+ x5 = 3
№ 16
x4 + x5 a max
= 1
x4 + 2⋅x5 = 12
+ x5 = 4
– x2 + 2⋅x3 – x4 + x5
+ x2 + x3
+ 2⋅x2 + x3 + x4 + x5
+ 2⋅x2
+ x5
3⋅x3
2⋅x1 + x2 + x3
+ 2⋅x3
3⋅x1
– x3
x1
№ 17
a max
= 2
= 11
= 6
№ 18
– 2⋅x4 – x5 a max
+ x4 + 3⋅x5 = 5
– x4 + 6⋅x5 = 7
+ 2⋅x4 + x5 = 2
№ 19
f(x) = x1 + 7⋅x2 + 2⋅x3 + x4 – x5 a max
6⋅x1 + 3⋅x2 + x3 + x4 + x5 = 20
= 12
+ x4
4⋅x1 + 3⋅x2
+ x5 = 6
3⋅x1 – 2⋅x2
∀ xj≥ 0
№ 20
f(x) = 2⋅x1
+ x3 – x4 + x5 a max
– x1 + 2⋅x2 + x3
= 2
3⋅x1 + 5⋅x2 + x3 + x4 + 2⋅x5 = 14
+ x5 = 1
x1 – x2
∀ xj ≥ 0
f(x) = 6⋅x1
– x1
2⋅x1
x1
∀ xj ≥ 0
f(x) =
∀ xj ≥ 0
№ 21
+ x2
+ x4 + 2⋅x5 a max
+ 2⋅x2 + x3
= 2
+ 6⋅x2 + 2⋅x3 + x4 + x5 = 18
– 2⋅x2
+ x5 = 2
3⋅x2 +
– x1 + 2⋅x2 +
x1 + x2
2⋅x1 + x2 +
+
f(x) = 3⋅x1
2⋅x1 + 2⋅x2 +
2⋅x1 – x2
x1 + x2
∀ xj ≥ 0
f(x) =
∀ xj≥ 0
f(x) =
∀ xj ≥ 0
5⋅x2 +
– x1 + x2 +
x1 – 2⋅x2
2⋅x1 + x2 +
x1
3⋅x1
– x1
3⋅x1
x3 – x4 + x5
x3
+ x4
x3 + x4 + 2⋅x5
№ 22
a max
= 2
= 2
= 6
№ 23
x3 – 2⋅x4 + x5 a max
x3 + x4 + x5 = 6
+ x4
= 2
+ x5 = 2
x3 –
x3
+
x3 +
№ 24
x4 + x5 a max
= 2
x4
= 2
x4 + 2⋅x5 = 10
+ 5⋅x2 + 2⋅x3 – x4 + x5
+ 4⋅x2 + x3
+ x2
+ x4
+ 2⋅x2 + x3 + x4 + x5
№ 25
a max
= 12
= 1
= 3
f(x) =
∀ xj ≥ 0
5⋅x1
x1
–3⋅x1
2⋅x1
№ 26
+ x3 – x4 + x5 a max
– x2 + x3
= 1
+ x2
+ x4
= 3
+ 2⋅x2 + x3 + x4 + 2⋅x5 = 12
№ 27
+ 2⋅x3 – x4 + x5 a max
f(x) = 7⋅x1
– x1 + x2 + x3
= 2
+ x4
= 3
3⋅x1 – x2
5⋅x1 + 2⋅x2 + x3 + x4 + x5 = 11
∀ xj ≥ 0
f(x) = x1
5⋅x1
– x1
3⋅x1
∀ xj ≥ 0
f(x) =
∀ xj ≥ 0
f(x) =
∀ xj ≥ 0
–
+
+
+
№ 28
+
x
+
x
+
x
4⋅x2
3
4
5 a max
+
x
+
+
x
5⋅x2
2⋅x4
3
5 = 28
+ x4
= 2
2⋅x2
+ x5 = 12
4⋅x2
8⋅x2 + 2⋅x3 + x4 – x5
– x1 + 2⋅x2 + x3
6⋅x1 + 3⋅x2 + x3 + x4 + x5
+ x5
3⋅x1 – 2⋅x2
№ 29
a max
= 2
= 20
= 6
№ 30
+
x
–
x
+
x
–2⋅x2
3
4
5 a max
+
+
x
+
x
+
5⋅x2
2⋅x5 = 14
3⋅x1
3
4
+ x4
= 10
2⋅x1 + 5⋅x2
x2
+ x5 = 1
x1 –
f(x) = 7⋅x1
– x1
3⋅x1
2⋅x1
∀ xj≥ 0
+
+
+
+
2⋅x2
2⋅x2 + x3
4⋅x2
6⋅x2 + 2⋅x3
№ 31
+ x4 + 2⋅x5 a max
+
= 2
+ x4
= 12
+ x4 + x5 = 18
№ 32
f(x) =
∀ xj ≥ 0
x1
– x1
2⋅x1
x1
f(x) = 5⋅x1
– x1
4⋅x1
x1
∀ xj ≥ 0
f(x) = x1
x1
x1
x1
∀ xj ≥ 0
+ 3⋅x2 + x3 – x4 + x5 a max
+ 2⋅x2 + x3 +
= 2
+ x2 + x3 + x4 + 2⋅x5 = 6
– x2
+ x5 = 1
№ 33
+ x2 – x3 + x4 + 2⋅x5 a max
+ 2⋅x2 + x3 +
= 2
+ x2 + x3 + 2⋅x4 + x5 = 8
+ x2
+ x5 = 2
№ 34
+ 2⋅x2 + x3 – x4 + x5 a max
+ x2 + 2⋅x3 + 2⋅x4 + x5 = 11
– 2⋅x2
+ x4
= 2
+ x2
+ x5 = 3
f(x) = 10⋅x1
2⋅x1
– x1
x1
∀ xj ≥ 0
+ 5⋅x2 + 2⋅x3 – x4 +
+ 3⋅x2 + x3 + 2⋅x4 +
+ x2
+ x4
– 3⋅x2
+
f(x) = 2⋅x1 – x2
x1
2⋅x1 + 2⋅x2
x1
∀ xj ≥ 0
f(x) = 4⋅x1
– x1
4⋅x1
3⋅x1
∀ xj≥ 0
№ 35
x5 a max
x5 = 17
= 1
x5 = 3
– 3⋅x3 + x4 + x5
+ 2⋅x3 + x4 + 3⋅x5
+ 4⋅x3 + 8⋅x4 + 4⋅x5
– x3 + 7⋅x4 + x5
– x2 + x3 + 2⋅x4 –
+ x2 + x3
+ 3⋅x2 + 2⋅x3 + x4 +
+ 2⋅x2
+
f(x) = 2⋅x1 + 2⋅x2 +
4⋅x1 – 3⋅x2 +
– x1 + 2⋅x2
x3 + 2⋅x4 –
x3
+ x4
№ 36
a max
= 6
= 16
= 7
№ 37
x5 a max
= 2
x5 = 13
x5 = 16
№ 38
x5 a max
= 12
= 2
∀ xj≥ 0
6⋅x1 + 3⋅x2 +
f(x) = 5⋅x1
9⋅x1
4⋅x1
3⋅x1
∀ xj ≥ 0
f(x) =
∀ xj ≥ 0
x1
2⋅x1
2⋅x1
x1
f(x) = –5⋅x1
3⋅x1
2⋅x1
3⋅x1
∀ xj ≥ 0
f(x) =
∀ xj ≥ 0
x3 +
+ 2⋅x2 – x3 +
+ x2 + x3 +
+ 3⋅x2
+
– 2⋅x2
x4 +
№ 39
x4 + x5 a max
x4 + 2⋅x5 = 26
x4
= 12
+ x5 = 6
+ 11⋅x2 + x3 + 2⋅x4 – x5
+ 6⋅x2 + x3 + x4 + x5
+ 5⋅x2
+ x4
–
x2
+ x5
+ x2
+ x2
+ 3⋅x2
+ x2
+ x3 –
– 3⋅x3 +
+ x3 +
– 2⋅x3 –
3⋅x2 +
2⋅x1 + x2 +
x1 + x2
x1 – x2
x5 = 26
№ 40
a max
= 13
= 10
= 1
№ 41
2⋅x4
a max
x4
= 1
2⋅x4 + x5 = 6
x4
= 2
№ 42
x3 – x4 + x5 a max
x3 + x4 + 2⋅x5 = 6
+ x4
= 2
+ x5 = 1
№ 43
f(x) = 8⋅x1 + x2 – 3⋅x3
a max
x1 + x2 + x3 + 2⋅x4 + x5 = 4
+ x3 – 3⋅x4 + 5⋅x5 = 3
2⋅x1
– x3 + 6⋅x4 + x5 = 6
3⋅x1
∀ xj ≥ 0
f(x) = 2⋅x1
– x1
x1
x1
+
+
+
+
№ 44
x2 + x3 – x4 + x5 a max
x2 + x3
= 2
x2 + 2⋅x3 + 2⋅x4 + x5 =11
x2
+ x5 = 3
∀ xj≥ 0
f(x) = 9⋅x1
3⋅x1
2⋅x1
x1
∀ xj ≥ 0
f(x) =
∀ xj ≥ 0
x1
x1
5⋅x1
2⋅x1
+
+
+
–
№ 45
+
–
x
+
x
5⋅x2
2⋅x3
4
5 a max
+
x
=12
4⋅x2
3
3⋅x2 + x3 + 2⋅x4 + x5 =17
+ x5 = 3
3⋅x2
№ 46
+ 3⋅x2 + x3 + x4 + x5 a max
– x2 + x3
= 1
+ 2⋅x2 + 2⋅x3 + x4 + 3⋅x5 =17
+ x2
+ x5 = 4
+ x3 + 2⋅x4 – x5
f(x) = 5⋅x1
4⋅x1 + 3⋅x2 + 2⋅x3 + x4 + x5
+ x4
3⋅x1 + x2
+ x5
3⋅x1 + 2⋅x2
∀ xj ≥ 0
f(x) =
∀ xj≥ 0
f(x) =
∀ xj ≥ 0
x1
4⋅x1
6⋅x1
3⋅x1
+ x2 + x3 + 2⋅x4 –
– 3⋅x2 + x3
+ 3⋅x2 + x3 + x4 +
+ 4⋅x2
+
№ 47
a max
=13
= 3
= 6
№ 48
x5 a max
=12
x5 =26
x5 =12
№ 49
– 7⋅x2 – x3 + x4 + x5 a max
–x1 + 2⋅x2 + x3
= 2
9⋅x1 + x2 + x3 + x4 + 2⋅x5 =26
+ x5 = 6
3⋅x1 – 2⋅x2
f(x) = 4⋅x1
–x1
2⋅x1
x1
∀ xj ≥ 0
+ 8⋅x2 + x3 + 2⋅x4 – x5
+ 2⋅x2 + x3
+ 6⋅x2 + x3 + x4 + x5
– x2
+ x5
№ 50
a max
= 2
=13
= 1
f(x) = 3⋅x1
x1
2⋅x1
3⋅x1
∀ xj ≥ 0
– x2 – x3 +
– x2
+
+ x2 + x3 +
+ 2⋅x2
–
№ 51
x4
a max
x4 + 2⋅x5 = 3
2⋅x4 + 3⋅x5 = 6
3⋅x4 + 8⋅x5 = 5
№ 52
f(x) = x1 – 3⋅x2 + x3 + 2⋅x4 – x5 a max
– x1 + 2⋅x2 + x3
= 2
+ x4
= 2
x1 + x2
x1 + 2⋅x2 + x3 + x4 + x5 = 5
∀ xj ≥ 0
№ 53
x2 + x3 – 2⋅x4 + x5 a max
f(x) =
= 2
– x1 + 2⋅x2 + x3
–
x
+
x
= 2
2⋅x1
2
4
2⋅x1 + 2⋅x2 + x3 + x4 + x5 = 6
∀ xj ≥ 0
№ 54
f(x) =
5⋅x2 + x3 – x4 + x5 a max
– x1 + x2 + x3
= 2
+ x4
= 2
x1 – 2⋅x2
x1 + x2 + 2⋅x3 + 2⋅x4 + x5 =11
∀ xj≥ 0
f(x) = 9⋅x1
3⋅x1
– x1
2⋅x1
∀ xj ≥ 0
f(x) =
∀ xj≥ 0
+ 2⋅x2 – x3
+ x5
+ 4⋅x2 + x3
+ x2
+ x4
+ 3⋅x2 + x3 + 2⋅x4 + x5
№ 55
a max
=12
= 1
=17
+ x3 + x4 + x5
x1
x1 – x2 + x3
+ x4
3⋅x1 + x2
5⋅x1 + 2⋅x2 + 2⋅x3 + x4 + 3⋅x5
№ 56
a max
= 1
= 3
=17
№ 57
f(x) = 3⋅x1
– x1
3⋅x1
4⋅x1
∀ xj≥ 0
– 2⋅x2 + x3 + 2⋅x4 – x5 a max
+ x2 + x3
= 2
– x2
+ x4
= 3
+ 3⋅x2 + 2⋅x3 + x4 + x5 =13
– x3 + x4 + x5
f(x) = 9⋅x1
– x1 + 2⋅x2 + x3
+ x4
4⋅x1 + 3⋅x2
9⋅x1 + x2 + x3 + x4 + 2⋅x5
∀ xj ≥ 0
f(x) = 5⋅x1
6⋅x1
– x1
3⋅x1
∀ xj ≥ 0
f(x) =
∀ xj ≥ 0
∀ xj ≥ 0
f(x) =
5⋅x2 + x3 + 2⋅x4 – x5
3⋅x2 + x3 + x4 + x5
+ x4
2⋅x2
+ x5
4⋅x2
№ 59
a max
=26
= 2
=12
№ 60
10⋅x2 + x3 + 2⋅x4 – x5 a max
– x1 + 2⋅x2 + x3
= 2
+ x4
=10
2⋅x1 + 5⋅x2
+
+
x
+
x
+
x
6⋅x2
2⋅x1
3
4
5 = 1
f(x) = 3⋅x1
3⋅x1
3⋅x1
7⋅x1
∀ xj ≥ 0
f(x) =
+
+
+
+
№ 58
a max
= 2
=12
=26
№ 61
+ 2⋅x2 + x3 – x4
a max
+ x2 + 3⋅x3 + x4 + 2⋅x5 = 5
+ 2⋅x2 + x3
+ x5 = 5
– 2⋅x2 + 2⋅x3
– x5 = 5
x1 + 2⋅x2
5⋅x1 + 10⋅x2
x2
6⋅x2
x1 +
2⋅x1 –
№ 62
– x3 –
x4
a max
+ 5⋅x3 + 15⋅x4 + 10⋅x5 =25
– x3 + 6⋅x4 + 2⋅x5 = 3
+ x3 –
x4 –
x5 = 5
x2 – 2⋅x3 –
x2
+
x4
x4 +
№ 63
a max
x5 = 4
3⋅x1 + 2⋅x2
x1 + x2 +
∀ xj≥ 0
f(x) =
∀ xj ≥ 0
+ x4 + x5 = 7
x3 + 2⋅x4 + 6⋅x5 = 9
x1 – 3⋅x2 + x3
2⋅x1 + x2 + x3
+ 2⋅x3
x1
+ 3⋅x3
3⋅x1
f(x) = –2⋅x1 – x2 + x3
3⋅x1 + x2 + x3
+ 3⋅x3
2⋅x1
– x3
3⋅x1
∀ xj≥ 0
№ 64
a max
+ x4 + x5 = 4
– x4 – 3⋅x5 = 3
+ x4 + 2⋅x5 = 6
№ 65
– 5⋅x4
a max
+ 2⋅x4 + 3⋅x5 = 7
+ 2⋅x4 – x5 = 1
+ x4 + 6⋅x5 = 9