The linear programming model below was formulated to maximize a company's profit subject to the constraints on two resources: 2- 20x, 40x. + 40x2 +10x3 + S₁ = 320 40 x + 20x2 + 40x² + ₂ = 360 Maximize z = 20x₁ + 10x₂ + 10x3 Subject to 40x1 + 40x2 + 10x3 ≤ 320, 40x1 + 20x2 + 40x3 ≤ 360, X; ≥ 0, i = 1, 2, 3. Z 1 - - 10x₂10x3 = 0 S -10 O 10 1 20 40 O 1 Solve the problem by using the Simplex algorithm. What are the values of the variables and the obiective function in the solution you found? -20 0 40 O 40 Xz -10 x3 RMS_ D 320 360
The linear programming model below was formulated to maximize a company's profit subject to the constraints on two resources: 2- 20x, 40x. + 40x2 +10x3 + S₁ = 320 40 x + 20x2 + 40x² + ₂ = 360 Maximize z = 20x₁ + 10x₂ + 10x3 Subject to 40x1 + 40x2 + 10x3 ≤ 320, 40x1 + 20x2 + 40x3 ≤ 360, X; ≥ 0, i = 1, 2, 3. Z 1 - - 10x₂10x3 = 0 S -10 O 10 1 20 40 O 1 Solve the problem by using the Simplex algorithm. What are the values of the variables and the obiective function in the solution you found? -20 0 40 O 40 Xz -10 x3 RMS_ D 320 360
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[simplex algorithm] this question requires to use matrix with slackness, I've already build the matrix but I dont know how to solve it. In this image 2, I used excel to figure out the solution, but how can I know that x2 is 0?
Transcribed Image Text:x3
x1
1.333333 7.666667
x2
profit
0 166.6667
![[Question 2]
(a) The linear programming model below was formulated to maximize a company's profit subject to
the constraints on two resources:
220x₁10x₂= 10x3 =O
40x. + 40x₂ + (0x3 + S₁ = 320
40 x₁ + 20x₂ + 40x³ + Sz
360
Sz
Maximize z = 20x₁ + 10x₂ + 10x3
Subject to
40x1 + 40x₂+ 10x3 ≤ 320,
40x1 + 20x₂ + 40x3 ≤ 360,
X₁ ≥ 0, i = 1, 2, 3.
Z
1
0
X,
-20
40
40
x z
-10
40
x3
-10
S,
7
10 1
20 40
RMS_
O
320
360
Solve the problem by using the Simplex algorithm. What are the values of the variables and the
objective function in the solution you found?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc76f7391-61d3-4396-8738-502514b3b1a1%2Fc4d2b0c5-5c0e-4c5e-bdde-f9f5db006821%2Flmg4zrf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:[Question 2]
(a) The linear programming model below was formulated to maximize a company's profit subject to
the constraints on two resources:
220x₁10x₂= 10x3 =O
40x. + 40x₂ + (0x3 + S₁ = 320
40 x₁ + 20x₂ + 40x³ + Sz
360
Sz
Maximize z = 20x₁ + 10x₂ + 10x3
Subject to
40x1 + 40x₂+ 10x3 ≤ 320,
40x1 + 20x₂ + 40x3 ≤ 360,
X₁ ≥ 0, i = 1, 2, 3.
Z
1
0
X,
-20
40
40
x z
-10
40
x3
-10
S,
7
10 1
20 40
RMS_
O
320
360
Solve the problem by using the Simplex algorithm. What are the values of the variables and the
objective function in the solution you found?
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