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4. (10 pts) Consider the following problem. Minimize Z=3x2+2 xZ+X3, Maximize subject...
(1 point) Consider the following maximization problem. Maximize P = 9x1 + 7x2 + x3 subject...
(1 point) Consider the following maximization problem. Maximize P = 9x1 + 7x2 + x3 subject to the constraints 13x1 x1 - x2 + 6x2 + - 10x3 12x3 = = 20 56 xi 20 x2 > 0 X3 > 0 Introduce slack variables and set up the initial tableau below. Keep the constraints in the same order as above, and do not rescale them. P X X2 X3 S1 RHS
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...
(4 points) Consider the following maximization problem. Maximize P = 14x + y - 10z subject...
(4 points) Consider the following maximization problem. Maximize P = 14x + y - 10z subject to the constraints 12x - y + x - 2y + 7x + 142 < 85 2z = 52 9z S 40 x>0 y> z> 0 Introduce slack variables (denoted u, V, and w) and set up the initial tableau below. Keep the constraints in the same order as above, and do not rescale them. Constant
d) Given the primal problem Max z= 8x/+3x2+xz Subject to: x;+6x,+8x3<118 X, + 5x+10x<240 X1, X2,X3,...
d) Given the primal problem Max z= 8x/+3x2+xz Subject to: x;+6x,+8x3<118 X, + 5x+10x<240 X1, X2,X3, 20 Write down its problem (5 marks) dual Question Nine R=622 R4 2 02. V-24V R = 422. R5=2.522. (a) What are the voltage across and the current in each of the resistors Ri through Rs in figure above? (6 Marks) (b) How much power is dissipated in R.? (4 marks)
Consider the following linear program: Maximize-2ri+ 2 subject to: 12x1 + 3x2 6, #7 10, i...
Consider the following linear program: Maximize-2ri+ 2 subject to: 12x1 + 3x2 6, #7 10, i 20 x2 20. a) Draw a graph of the constraints and shade in the feasible region. Label the vertices of this region with their coordinates. b) Using the graph obtained in (a). find the optimal solution and the maximum value of the objective function. c) What is the slack in each of the constraints?
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...
4.3-7. Consider the following problem. Maximize Z = 5x1 + 3x2 + 4x3, subject to 2x1 + x2 + x3<...
4.3-7. Consider the following problem. Maximize Z = 5x1 + 3x2 + 4x3, subject to 2x1 + x2 + x3<= 20 3x1 + x2 + 2x3 <= 30 and x1 >= 0, x2 >= 0, x3 >= 0. You are given the information that the nonzero variables in the optimal solution are x2 and x3. (a) Describe how you can use this information to adapt the simplex method to solve this problem in the minimum possible number of iterations (when...
*5. Solve the following LP problem using two-phase Simplex method: Maximize f- 4x1x2 X3 subject to...
*5. Solve the following LP problem using two-phase Simplex method: Maximize f- 4x1x2 X3 subject to 2х1 + X2 + 2хз - 4, Зх1 + 3x2 + хз 3 3, х120, х2 2 0, хз 2 0. Note: Since a BFS is not available, start Phase I simplex algorithm by introducing two artificial variables]
*5. Solve the following LP problem using two-phase Simplex method: Maximize f- 4x1x2 X3 subject to 2х1 + X2 + 2хз - 4, Зх1 + 3x2...
[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...
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...
(1 point) Consider the following maximization problem. Maximize P = 9x1 + 7x2 + x3 subject to the constraints 13x1 x1 - x2 + 6x2 + - 10x3 12x3 = = 20 56 xi 20 x2 > 0 X3 > 0 Introduce slack variables and set up the initial tableau below. Keep the constraints in the same order as above, and do not rescale them. P X X2 X3 S1 RHS
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...
(4 points) Consider the following maximization problem. Maximize P = 14x + y - 10z subject to the constraints 12x - y + x - 2y + 7x + 142 < 85 2z = 52 9z S 40 x>0 y> z> 0 Introduce slack variables (denoted u, V, and w) and set up the initial tableau below. Keep the constraints in the same order as above, and do not rescale them. Constant
d) Given the primal problem Max z= 8x/+3x2+xz Subject to: x;+6x,+8x3<118 X, + 5x+10x<240 X1, X2,X3, 20 Write down its problem (5 marks) dual Question Nine R=622 R4 2 02. V-24V R = 422. R5=2.522. (a) What are the voltage across and the current in each of the resistors Ri through Rs in figure above? (6 Marks) (b) How much power is dissipated in R.? (4 marks)
Consider the following linear program: Maximize-2ri+ 2 subject to: 12x1 + 3x2 6, #7 10, i 20 x2 20. a) Draw a graph of the constraints and shade in the feasible region. Label the vertices of this region with their coordinates. b) Using the graph obtained in (a). find the optimal solution and the maximum value of the objective function. c) What is the slack in each of the constraints?
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. Solve the following LP problem using two-phase Simplex method: Maximize f- 4x1x2 X3 subject to 2х1 + X2 + 2хз - 4, Зх1 + 3x2 + хз 3 3, х120, х2 2 0, хз 2 0. Note: Since a BFS is not available, start Phase I simplex algorithm by introducing two artificial variables]
*5. Solve the following LP problem using two-phase Simplex method: Maximize f- 4x1x2 X3 subject to 2х1 + X2 + 2хз - 4, Зх1 + 3x2...
[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...
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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