# MATH 132-Costraints Simplex Methods Questions-UNLV .

9/23/21, 5:50 PM Quiz: 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 https://unlv.instructure.com/courses/102986/quizzes/367212/take 1/14 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 https://unlv.instructure.com/courses/102986/quizzes/367212/take 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 https://unlv.instructure.com/courses/102986/quizzes/367212/take 3/14 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 https://unlv.instructure.com/courses/102986/quizzes/367212/take 4/14 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 = https://unlv.instructure.com/courses/102986/quizzes/367212/take 5/14 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 = https://unlv.instructure.com/courses/102986/quizzes/367212/take 6/14 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 = https://unlv.instructure.com/courses/102986/quizzes/367212/take 7/14 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 https://unlv.instructure.com/courses/102986/quizzes/367212/take 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 = https://unlv.instructure.com/courses/102986/quizzes/367212/take 9/14 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 = https://unlv.instructure.com/courses/102986/quizzes/367212/take 10/14 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 https://unlv.instructure.com/courses/102986/quizzes/367212/take 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 = https://unlv.instructure.com/courses/102986/quizzes/367212/take 12/14 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 = https://unlv.instructure.com/courses/102986/quizzes/367212/take 13/14 9/23/21, 5:50 PM Quiz: Section 5.1 a44 = a45 = a46 = a47 = a48 = Quiz saved at 5:50pm https://unlv.instructure.com/courses/102986/quizzes/367212/take Submit Quiz 14/14