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3. Consider the following LP. Maximize u = 4x1 + 2x2 subject to X1 + 2x2...
Find all the basic solutions for the following LP problems using the Gauss– Jordan elimination method....
Find all the basic solutions for the following LP problems using the Gauss– Jordan elimination method. Identify basic feasible solutions and show them on graph paper. Maximize z = 4x1 + 2x2 subject to −2x1 + x2 ≤ 4 x1 + 2x2 ≥ 2 x1, x2 ≥ 0
QUESTION 15 Describe the solution space for the following LP model: Maximize: 2x1 3x2 Subject to:...
QUESTION 15 Describe the solution space for the following LP model: Maximize: 2x1 3x2 Subject to: 1: 2x1 3x2 2 18 2: 4x1 2x2 2 10 x1, x2 20 Multiple optimal solutions O Infeasible None of the above QUESTION 16 Describe the solution for the folowing LP model: Maximize: 2x1 3x2 Subject to: 1:4x1 +5x2 2 20 2: 3x1 2x2 212 x1, x2 20 A single optimal solution O Infeasible Multiple optimal solutions None of the above QUESTION 17 In...
Use the simplex algorithm to find all optimal solutions to the following LP. max z=2x1+x2 s.t....
Use the simplex algorithm to find all optimal solutions to the following LP. max z=2x1+x2 s.t. 4x1 + 2x2 ≤ 4 −2x1 + x2 ≤ 2 x1 ≥1 x1,x2 ≥0
5. Solve the following LP problem using Phase I and Phase II simplex algorithm. Maximize f(X)...
5. Solve the following LP problem using Phase I and Phase II simplex algorithm. Maximize f(X) = x1 + x2, subject to: 4x1-2x2 8 XI6 X1, X20
5. Solve the following LP problem using Phase I and Phase II simplex algorithm. Maximize f(X) = x1 + x2, subject to: 4x1-2x2 8 XI6 X1, X20
Consider the following LP: Max x1 +x2 +x3 s.t. x1 +2x2 +2x3 ≤ 20 Solve this...
Consider the following LP: Max x1 +x2 +x3 s.t. x1 +2x2 +2x3 ≤ 20 Solve this problem without using the simplex algorithm, but using the fact that an optimal solution to LP exists at one of the basic feasible solutions.
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2,...
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2, X320 (a) Convert the above constraints to equalities. (2 marks) (b) Set up the initial simplex tableau and solve. (9 marks)
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2, X320 (a) Convert the above constraints to equalities. (2 marks) (b) Set up the initial simplex tableau and solve. (9 marks)
e the simplex method to maximize P= 7x1 + 13x2 subject to 4x1 x1 + +...
e the simplex method to maximize P= 7x1 + 13x2 subject to 4x1 x1 + + x2 4x2 = = 8 12 x120 x2 > 0 P=
[4.37] Consider the following problem: Maximize 2x + 3x2 subject to X1 + 2x2 5 10...
[4.37] Consider the following problem: Maximize 2x + 3x2 subject to X1 + 2x2 5 10 -*1 + 2x2 s 6 *1 + *2 S6 12 0. a. c. X1, Solve the problem graphically and verify that the optimal point is a degenerate basic feasible solution. b. Solve the problem by the simplex method. From Part (a), identify the constraint that causes degeneracy and resolve the problem after deleting this constraint. Note that degeneracy disappears and the same optimal solution...
3. Use the two-phase simplex method to solve the following LP. Min z = x1 +...
3. Use the two-phase simplex method to solve the following LP. Min z = x1 + 2x2 Subject to 3x1 + 4x2 < 12 2x1 - x2 2 2 X1, X2 20
4.6-1.* Consider the following problem. Maximize Z= 2x1 + 3x2, subject to x1 + 2x2 54...
4.6-1.* Consider the following problem. Maximize Z= 2x1 + 3x2, subject to x1 + 2x2 54 x1 + x2 = 3 and X120, X2 0. DI (a) Solve this problem graphically. (b) Using the Big M method, construct the complete first simplex tableau for the simplex method and identify the corresponding initial (artificial) BF solution. Also identify the initial entering basic variable and the leaving basic variable. I (c) Continue from part (b) to work through the simplex method step...
QUESTION 15 Describe the solution space for the following LP model: Maximize: 2x1 3x2 Subject to: 1: 2x1 3x2 2 18 2: 4x1 2x2 2 10 x1, x2 20 Multiple optimal solutions O Infeasible None of the above QUESTION 16 Describe the solution for the folowing LP model: Maximize: 2x1 3x2 Subject to: 1:4x1 +5x2 2 20 2: 3x1 2x2 212 x1, x2 20 A single optimal solution O Infeasible Multiple optimal solutions None of the above QUESTION 17 In...
5. Solve the following LP problem using Phase I and Phase II simplex algorithm. Maximize f(X) = x1 + x2, subject to: 4x1-2x2 8 XI6 X1, X20
5. Solve the following LP problem using Phase I and Phase II simplex algorithm. Maximize f(X) = x1 + x2, subject to: 4x1-2x2 8 XI6 X1, X20
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2, X320 (a) Convert the above constraints to equalities. (2 marks) (b) Set up the initial simplex tableau and solve. (9 marks)
Consider the following linear program: Maximize Z-3xI+2x2-X3 Subject to:X1+X2+2 X3s 10 2x1-X2+X3 s20 3 X1+X2s15 X1, X2, X320 (a) Convert the above constraints to equalities. (2 marks) (b) Set up the initial simplex tableau and solve. (9 marks)
e the simplex method to maximize P= 7x1 + 13x2 subject to 4x1 x1 + + x2 4x2 = = 8 12 x120 x2 > 0 P=
[4.37] Consider the following problem: Maximize 2x + 3x2 subject to X1 + 2x2 5 10 -*1 + 2x2 s 6 *1 + *2 S6 12 0. a. c. X1, Solve the problem graphically and verify that the optimal point is a degenerate basic feasible solution. b. Solve the problem by the simplex method. From Part (a), identify the constraint that causes degeneracy and resolve the problem after deleting this constraint. Note that degeneracy disappears and the same optimal solution...
3. Use the two-phase simplex method to solve the following LP. Min z = x1 + 2x2 Subject to 3x1 + 4x2 < 12 2x1 - x2 2 2 X1, X2 20
4.6-1.* Consider the following problem. Maximize Z= 2x1 + 3x2, subject to x1 + 2x2 54 x1 + x2 = 3 and X120, X2 0. DI (a) Solve this problem graphically. (b) Using the Big M method, construct the complete first simplex tableau for the simplex method and identify the corresponding initial (artificial) BF solution. Also identify the initial entering basic variable and the leaving basic variable. I (c) Continue from part (b) to work through the simplex method step...
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