UNLV MATH 132 Costraints Simplex Methods Questions

9/23/21, 5:50 PMQuiz: Section 5.1
Section 5.1
Started: Sep 21 at 9:18pm
Quiz Instructions
Question 1
2 pts
In the simplex method, which of the following is considered a Standard Maximum
problem? (Please select one answer).
Maximize:
P = 40×1 + 30×2
Subject to the following constraints:
x1 + 2×2 ≤ −16
x1 + x2 ≤ −9
3×1 + 2×2 ≤ −24
x1 ≥ 0
;
Maximize: Z
x2 ≥ 0
= 4 x1 + 6 x2
Subject to the following constraints:
−x1 + x2 ≥ 11
x1 + x2 ≥ 27
2×1 + 5×2 ≤ 90
x1 ≥ 0
;
Maximize: P
x2 ≥ 0
= 4×1 + 5×2
Subject to the following constraints:
x1 + x2 ≤ 10
3×1 + 7×2 ≤ 42
x1 ≤ 0
;
Maximize: Z
x2 ≥ 0
= x1 + 7×2
Subject to the following constraints:
3×1 + 2×2 ≤ 60
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9/23/21, 5:50 PM
Quiz: Section 5.1
x1 + 2×2 ≥ 28
x1 + 4×2 ≤ 48
x1 ≥ 0
;
Maximize:
x2 ≥ 0
P = −x1 + 2×2 + 3×3
Subject to the following constraints:
x1 + 2×2 + 2×3 ≤ −20
5×1 − 2×2 + 4×3 ≤ 15
2×1 + 2×2 + 4×3 ≤ 23
x1 ≥ 0
;
x2 ≥ 0
;
x3 ≥ 0
Maximize:
Z = 2×1 − x2 + 2×3
Subject to the following constraints:
2×1 + x2 ≤ 10
x1 + 2×2 − 2×3 ≤ 20
x1 + 2×2 − 2×3 ≤ 20
x1 ≥ 0
;
Maximize: Z
x2 ≥ 0
;
x3 ≤ 0
= 6×1 + 8×2
Subject to the following constraints:
5×1 + 10×2 ≤ 60
4×1 + 4×2 ≤ −40
x1 ≥ 0
;
Maximize:
x2 ≥ 0
P = 6×1 + 5×2 + 4×3
Subject to the following constraints:
2×1 + x2 + x3 ≤ 180
x1 + 3×2 + 2×3 ≤ 300
2×1 + x2 + 2×3 ≤ 240
x1 ≥ 0
;
x2 ≥ 0
;
x3 ≥ 0
Question 2
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2 pts
2/14
9/23/21, 5:50 PM
Quiz: Section 5.1
In the simplex method, which of the following is considered a Standard Maximum
problem? (Please select one answer).
Maximize: Z
=
x1 − x2 + x3
Subject to the following constraints:
2×1 + x2 − 3×3 ≥ 40
x1 + x3 ≥ 25
2×2 + 3×3 ≤ 32
x1 ≥ 0
;
Maximize: Z
x2 ≥ 0
;
x3 ≥ 0
= 2×1 + x2
Subject to the following constraints:
x1 + x2 ≤ 10
−x1 + x2 ≥ 2
x1 ≥ 0
;
x2 ≥ 0
Maximize: P
= x1 + x2
Subject to the following constraints:
x1 + 2×2 ≤ 6
2×1 − x2 ≤ −1
x1 ≤ 0
;
Maximize: Z
x2 ≥ 0
= 6×1 + 8×2
Subject to the following constraints:
5×1 + 10×2 ≤ 60
4×1 + 4×2 ≤ −40
x1 ≥ 0
;
Maximize:
x2 ≥ 0
P = −x1 + 2×2 + 3×3
Subject to the following constraints:
x1 + 2×2 + 2×3 ≤ −20
5×1 − 2×2 + 4×3 ≤ 15
2×1 + 2×2 + 4×3 ≤ 23
x1 ≥ 0
;
x2 ≥ 0
;
x3 ≥ 0
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9/23/21, 5:50 PM
Quiz: Section 5.1
Maximize:
Z = 2×1 − x2 + 2×3
Subject to the following constraints:
2×1 + x2 ≤ 10
x1 + 2×2 − 2×3 ≤ 20
x1 + 2×2 − 2×3 ≤ 20
x1 ≥ 0
;
x2 ≥ 0
;
Maximize:
P = 40×1 + 30×2
x3 ≤ 0
Subject to the following constraints:
x1 + 2×2 ≤ −16
x1 + x2 ≤ −9
3×1 + 2×2 ≤ −24
x1 ≥ 0
;
Maximize:
x2 ≥ 0
P = 40×1 + 30×2
Subject to the following constraints:
x1 + 2×2 ≤ 16
x1 + x2 ≤ 9
3×1 + 2×2 ≤ 24
x1 ≥ 0
;
x2 ≥ 0
Question 3
5 pts
Given the following maximum problem:
Maximize:
P = 4x 1 + 6x 2
Subject to the following constraints:
⎧ −x 1 + x 2 ≤ 11
⎪
⎪
⎪
⎪ x + x ≤ 27
⎪
1
2
⎨ 2x 1 + 5x 2 ≤ 90
⎪
⎪
⎪ x1 ≥ 0
⎪
⎩
⎪
x2 ≥ 0
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9/23/21, 5:50 PM
Quiz: Section 5.1
the Initial Simplex Tableau can be formatted in this form:
⎡
P
x1
x2
s1
s2
s3
RH S
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
a11
a12
a13
a14
a15
a16
a17
a21
a22
a23
a24
a25
a26
a27
a31
a32
a33
a34
a35
a36
a37
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
a41
a42
a43
a44
a45
a46
a47
⎣
⎦
In each box below, enter the appropriate value that must replace each of the letters
a11 through
a47 in the above tableau.
a11 =
a12 =
a13 =
a14 =
a15 =
a16 =
a17 =
a21 =
a22 =
a23 =
a24 =
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9/23/21, 5:50 PM
Quiz: Section 5.1
a25 =
a26 =
a27 =
a31 =
a32 =
a33 =
a34 =
a35 =
a36 =
a37 =
a41 =
a42 =
a43 =
a44 =
a45 =
a46 =
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9/23/21, 5:50 PM
Quiz: Section 5.1
a47 =
Question 4
5 pts
Given the following maximum problem:
Maximize:
P = x 1 + 2x 2
Subject to the following constraints:
⎧ x 1 + 3x 2 ≤ 15
⎪
⎪
2x 1 − x 2 ≤ 12
⎨
x1 ≥ 0
⎪
⎩
⎪
x2 ≥ 0
the Initial Simplex Tableau can be formatted in this form:
⎡
P
x1
x2
s1
s2
RH S
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎢
a11
a12
a13
a14
a15
a16
a21
a22
a23
a24
a25
a26
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎣
a31
a32
a33
a34
a35
a36
⎦
In each box below, enter the appropriate value that must replace each of the letters
a11 through
a36 in the above tableau.
a11 =
a12 =
a13 =
a14 =
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9/23/21, 5:50 PM
Quiz: Section 5.1
a15 =
a16 =
a21 =
a22 =
a23 =
a24 =
a25 =
a26 =
a31 =
a32 =
a33 =
a34 =
a35 =
a36 =
Question 5
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5 pts
8/14
9/23/21, 5:50 PM
Quiz: Section 5.1
Given the following maximum problem:
Maximize:
P = 2x 1 − x 2 + 2x 3
Subject to the following constraints:
⎧ 2x 1 + x 2 ≤ 10
⎪
⎪
⎪
⎪
⎪ x 1 + 2x 2 − 2x 3 ≤ 20
⎪
⎪
x 2 + 2x 3 ≤ 5
⎨
⎪ x1 ≥ 0
⎪
⎪
⎪
⎪
x2 ≥ 0
⎪
⎩
⎪
x3 ≥ 0
the Initial Simplex Tableau can be formatted in this form:
⎡
P
x1
x2
x3
s1
s2
s3
RH S
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
a11
a12
a13
a14
a15
a16
a17
a18
a21
a22
a23
a24
a25
a26
a27
a28
a31
a32
a33
a34
a35
a36
a37
a38
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
a41
a42
a43
a44
a45
a46
a47
a48
⎣
⎦
In each box below, enter the appropriate value that must replace each of the letters
a11
through
a48
in the above tableau.
a11 =
a12 =
a13 =
a14 =
a15 =
a16 =
a17 =
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9/23/21, 5:50 PM
Quiz: Section 5.1
a18 =
a21 =
a22 =
a23 =
a24 =
a25 =
a26 =
a27 =
a28 =
a31 =
a32 =
a33 =
a34 =
a35 =
a36 =
a37 =
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9/23/21, 5:50 PM
Quiz: Section 5.1
a38 =
a41 =
a42 =
a43 =
a44 =
a45 =
a46 =
a47 =
a48 =
Question 6
5 pts
Given the following maximum problem:
Maximize: P
= 5x 1 + 2x 2 + 8x 3
Subject to the following constraints:
⎧ 2x 1 − 4x 2 + x 3 ≤ 42
⎪
⎪
⎪
⎪
⎪ 2x 1 + 3x 2 − x 3 ≤ 42
⎪
⎪
6x 1 − x 2 + 3x 3 ≤ 42
⎨
x1 ≥ 0
⎪
⎪
⎪
⎪x ≥ 0
⎪
2
⎪
⎩
⎪
x3 ≥ 0
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11/14
9/23/21, 5:50 PM
Quiz: Section 5.1
the Initial Simplex Tableau can be formatted in this form:
⎡
P
x1
x2
x3
s1
s2
s3
RH S
⎤
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
⎢
a11
a12
a13
a14
a15
a16
a17
a18
a21
a22
a23
a24
a25
a26
a27
a28
a31
a32
a33
a34
a35
a36
a37
a38
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
⎥
a41
a42
a43
a44
a45
a46
a47
a48
⎣
⎦
In each box below, enter the appropriate value that must replace each of the letters
a11
through
a48
in the above tableau.
a11 =
a12 =
a13 =
a14 =
a15 =
a16 =
a17 =
a18 =
a21 =
a22 =
a23 =
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9/23/21, 5:50 PM
Quiz: Section 5.1
a24 =
a25 =
a26 =
a27 =
a28 =
a31 =
a32 =
a33 =
a34 =
a35 =
a36 =
a37 =
a38 =
a41 =
a42 =
a43 =
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9/23/21, 5:50 PM
Quiz: Section 5.1
a44 =
a45 =
a46 =
a47 =
a48 =
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