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S- In the optimal table of the simplex for the following linear programming problem x1, x3,...
5. Suppose that (x1, X2, X3) is a feasible solution to the linear programming problem 4r,...
5. Suppose that (x1, X2, X3) is a feasible solution to the linear programming problem 4r, +2x2 + x3 minimize X12 3, 2a 23 2 4, subject to Let y and ybe non-negative numbers (a) Show that x1(y2y2)2(-y12) + x3y2 2 3y14y2 1 (b) Find constraints on yi and y2 so that 4x12 2 x1(y1 + 2¥2) + x2(-y1 + Y2) + x3Y2 1 at every feasible solution (xi, x2, X3) (c) Use parts (a) and (b) to find a...
Use the simplex method to solve this problem Objective Function (OF) Max Z = 5x1 +...
Use the simplex method to solve this problem
Objective Function (OF)
Max Z = 5x1 + 3x2 + x3
Restrictions
x1 + x2 +
x36
5x1 + 3x2 + 6x315
Xi0
2- The following linear programming problem maximizes the profit in a manufacturing setup. Suppose that the...
2- The following linear programming problem maximizes the profit in a manufacturing setup. Suppose that the first and second constraints show the labor and material constraint, respectively max z = 4x + 3x, +5x, S.T. x + 2x + 3x, 39 +3x, + x, 312 *.*, 20 Optimal table: NS RHS 6/5 X3 1/5 2/5 -1/5 3/5 X1 -1/5 27/5 O 18/5 6/5 - 1) Fill the blank cells in the table using Simplex Matrix Math. 2) Find the range...
Question 1 - Revised Simplex Algorithm 10 marks Suppose we are solving the following linear programming problem Subject...
Question 1 - Revised Simplex Algorithm 10 marks Suppose we are solving the following linear programming problem Subject to 8x1 + 12x2 + x3 15x2 + x4 3x1 + 6x2 + X5 -120 60 = 48 x1,x2,x3, x4,x5 2 0 Assume we have a current basis of x2,xz, x5. Demonstrate your understanding of the steps of the Revised Simplex Algorithm by answering the following: a) What is the basic feasible solution at this stage? What is the value of the...
You are given the following linear programming model in algebraic form, with X1 and X2 as...
You are given the following linear programming model in algebraic form, with X1 and X2 as the decision variables: Note: Each part is independent (i.e., any change made in one problem part does not apply to any other parts). Minimize 40X1+50X2 Subject to 2X1+3X2>=30 2 X1+ X2>=20 X1>=0, X2>=0 a) Graph the feasible region and label the corner point. Compute the optimal solution using any method of your choice. Justify your answer and indicate the optimal solution on your graph....
Solve the linear programming problem using the simplex method Maximize P=2x2 + 3x2 + 4x3 subject...
Solve the linear programming problem using the simplex method Maximize P=2x2 + 3x2 + 4x3 subject to X1 + x3 s 12 X2 + x3 s 9 *2, X2, X3 20 Use the simplex method to solve the problem. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The maximum value of Pis when xy = X2 and x3 = OB. There is no optimal solution
Consider the following linear programming problem. Maximize 5X1 + 3X2 Subject to: X1 + X2 ≤...
Consider the following linear programming problem. Maximize 5X1 + 3X2 Subject to: X1 + X2 ≤ 20 X1 ≥ 5 X2 ≤ 10 X1, X2 ≥ 0 What are the optimal values of X1 and X2 respectively?
Convert the following formulation to a 2 variable problem so that it can be solved graphically...
Convert the following formulation to a 2 variable problem so
that it can be solved graphically (HINT: Eliminate one of the
variables – say X3...). Sketch the feasible region and compute the
coordinates of its extreme points.
5X1 + X3
17
2X1 + 1.5X2 + X3
14
.5X1 + 2X2 + X3
10
X1 , X2 , X3
0
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable...
SOLVE STEP BY STEP! 4. Consider the following LP: Minimize z = x; +3x2 - X3...
SOLVE STEP BY STEP!
4. Consider the following LP: Minimize z = x; +3x2 - X3 Subject to x + x2 + x2 > 3 -x + 2xz > 2 -x + 3x2 + x3 34 X1 X2,43 20 (a) Using the two-phase method, find the optimal solution to the primal problem above. (b) Write directly the dual of the primal problem, without using the method of transformation. (c) Determine the optimal values of the dual variables from the optimal...
Problem #5 -- Consider the following linear programming problem: Maximize Z = 2x1 + 4x2 +...
Problem #5 -- Consider the following linear programming problem: Maximize Z = 2x1 + 4x2 + 3x3 subject to: X1 + 3x2 + 2x3 S 30 best to X1 + x2 + x3 S 24 3x1 + 5x2 + 3x3 5 60 and X120, X220, X3 2 0. You are given the information that x > 0, X2 = 0, and x3 >O in the optimal solution. Using the given information and the theory of the simplex method, analyze the...
5. Suppose that (x1, X2, X3) is a feasible solution to the linear programming problem 4r, +2x2 + x3 minimize X12 3, 2a 23 2 4, subject to Let y and ybe non-negative numbers (a) Show that x1(y2y2)2(-y12) + x3y2 2 3y14y2 1 (b) Find constraints on yi and y2 so that 4x12 2 x1(y1 + 2¥2) + x2(-y1 + Y2) + x3Y2 1 at every feasible solution (xi, x2, X3) (c) Use parts (a) and (b) to find a...
Use the simplex method to solve this problem
Objective Function (OF)
Max Z = 5x1 + 3x2 + x3
Restrictions
x1 + x2 +
x36
5x1 + 3x2 + 6x315
Xi0
2- The following linear programming problem maximizes the profit in a manufacturing setup. Suppose that the first and second constraints show the labor and material constraint, respectively max z = 4x + 3x, +5x, S.T. x + 2x + 3x, 39 +3x, + x, 312 *.*, 20 Optimal table: NS RHS 6/5 X3 1/5 2/5 -1/5 3/5 X1 -1/5 27/5 O 18/5 6/5 - 1) Fill the blank cells in the table using Simplex Matrix Math. 2) Find the range...
Question 1 - Revised Simplex Algorithm 10 marks Suppose we are solving the following linear programming problem Subject to 8x1 + 12x2 + x3 15x2 + x4 3x1 + 6x2 + X5 -120 60 = 48 x1,x2,x3, x4,x5 2 0 Assume we have a current basis of x2,xz, x5. Demonstrate your understanding of the steps of the Revised Simplex Algorithm by answering the following: a) What is the basic feasible solution at this stage? What is the value of the...
Solve the linear programming problem using the simplex method Maximize P=2x2 + 3x2 + 4x3 subject to X1 + x3 s 12 X2 + x3 s 9 *2, X2, X3 20 Use the simplex method to solve the problem. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The maximum value of Pis when xy = X2 and x3 = OB. There is no optimal solution
Convert the following formulation to a 2 variable problem so
that it can be solved graphically (HINT: Eliminate one of the
variables – say X3...). Sketch the feasible region and compute the
coordinates of its extreme points.
5X1 + X3
17
2X1 + 1.5X2 + X3
14
.5X1 + 2X2 + X3
10
X1 , X2 , X3
0
We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable...
SOLVE STEP BY STEP!
4. Consider the following LP: Minimize z = x; +3x2 - X3 Subject to x + x2 + x2 > 3 -x + 2xz > 2 -x + 3x2 + x3 34 X1 X2,43 20 (a) Using the two-phase method, find the optimal solution to the primal problem above. (b) Write directly the dual of the primal problem, without using the method of transformation. (c) Determine the optimal values of the dual variables from the optimal...
Problem #5 -- Consider the following linear programming problem: Maximize Z = 2x1 + 4x2 + 3x3 subject to: X1 + 3x2 + 2x3 S 30 best to X1 + x2 + x3 S 24 3x1 + 5x2 + 3x3 5 60 and X120, X220, X3 2 0. You are given the information that x > 0, X2 = 0, and x3 >O in the optimal solution. Using the given information and the theory of the simplex method, analyze the...
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