Problem 3: Consider the following LP. (a) Solve the LP with the graphical method. (b) Place...
Problem 3: Consider the following LP.
(a) Solve the LP with the graphical method.
(b) Place the model in standard form.
(c) Use a simplex algorithm in tableau form and solve the LP.
(d) Using matrix A and b recalculate the basic feasible solution and the directions for the first iteration.
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Problem 3: Consider the following LP.
(a) Solve the LP with the graphical method.
(b) Place...
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.
3. Solve the accompanying LP using the Big M Method. A Convert the problem into the...
3. Solve the accompanying LP using the Big M Method. A Convert the problem into the standard form, including the artificial variables. s.t. B. Modify the objective function and eliminate the artificial variables) C. Solve the problem using the simplex algorithm.
#16.2 Consider the following standard form LP problem: minimize 2xi -x2-^3 subject to 3x1+x2+エ4-4 a. Write down the A,...
#16.2 Consider the following standard form LP problem: minimize 2xi -x2-^3 subject to 3x1+x2+エ4-4 a. Write down the A, b, and c matrices/vectors for the problem. b. Consider the basis consisting of the third and fourth columns of A, or- dered according to [a4, as]. Compute the canonical tableau correspond ing to this basis c. Write down the basic feasible solution corresponding to the basis above, and its objective function value. d. Write down the values of the reduced cost...
Consider the following problem Minimize Z3x+2 subject to 3+26 and 20, 20 ()Solve this problem graphically...
Consider the following problem Minimize Z3x+2 subject to 3+26 and 20, 20 ()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. (c) Work through the simplex method step by step to solve the problem
Find solution using Simplex method (BigM method) MAX Z = 5x1 + 3x2 + 2x3 +...
Find solution using Simplex method (BigM method) MAX Z = 5x1 + 3x2 + 2x3 + 4x4 subject to 5x1 + x2 + x3 + 8x4 = 10 2x1 + 4x2 + 3x3 + 2x4 = 10 X j > 0, j=1,2,3,4 a) make the necessary row reductions to have the tableau ready for iteration 0. On this tableau identify the corresponding initial (artificial) basic feasible solution. b) Following the result obtained in (a) solve by the Simplex method, using...
Exercise 1. Please use the simplex method to solve the below LP min z=3.r - 12...
Exercise 1. Please use the simplex method to solve the below LP min z=3.r - 12 s.t. 21; +12<8 21 +225 21 - 22 S4 21,220 a) Write the LP in standard form. b) Provide tableaus, BV, NBV, solution, objective value for each iteration of the simplex method. (Hint: the optimal value z=-5).
Exercise 1. Please use the simplex method to solve the below LP min z=3.r - 12...
Exercise 1. Please use the simplex method to solve the below LP min z=3.r - 12 s.t. 21; +12<8 21 +225 21 - 22 S4 21,220 a) Write the LP in standard form. b) Provide tableaus, BV, NBV, solution, objective value for each iteration of the simplex method. (Hint: the optimal value z=-5).
Problem 2: (This is from Problems 4 and 5. Page 172 of the textbook) (a) Use...
Problem 2: (This is from Problems 4 and 5. Page 172 of the textbook) (a) Use Phase I Simplex Algorithm to find an initial basic feasible solution. Next, use the Simplex Tableau Method to solve this problem. Show that if ties are broken in favor of lower-numbered rows, then cycling occurs when the Simplex method is used to solve the following LP: max z-3x1 +x2 - 6x3 9x1 x2 -9x3 -2 x40 xi + (1/3)X2 - 2x3 - (1/3)X0 9x1...
(3) Kyle gave Cartman the tableau of a max-LP to solve using the simplex method. The LP had two variables (x1, 22) and two < constraints. Cartman decided to play a joke on Kyle, so he (a) chan...
(3) Kyle gave Cartman the tableau of a max-LP to solve using the simplex method. The LP had two variables (x1, 22) and two < constraints. Cartman decided to play a joke on Kyle, so he (a) changed the coefficient of zi in the first constraint from 6 to 9, and (b) solved the LP as a min-LP With these modifications, Cartman got the following"optimal" tableau after performing a single pivot. Find the correct optimal tableau that Kyle should have...
Exercise 1. Please use the simplex method to solve the below LP min 2=3.01 - 22...
Exercise 1. Please use the simplex method to solve the below LP min 2=3.01 - 22 s.t. 2.c +228 2 + xy S5 21 - 22<4 2,220 a) Write the LP in standard form. b) Provide tableaus, BV, NBV, solution, objective value for each iteration of the simplex method. (Hint: the optimal value z=-5).
3. Solve the accompanying LP using the Big M Method. A Convert the problem into the standard form, including the artificial variables. s.t. B. Modify the objective function and eliminate the artificial variables) C. Solve the problem using the simplex algorithm.
#16.2 Consider the following standard form LP problem: minimize 2xi -x2-^3 subject to 3x1+x2+エ4-4 a. Write down the A, b, and c matrices/vectors for the problem. b. Consider the basis consisting of the third and fourth columns of A, or- dered according to [a4, as]. Compute the canonical tableau correspond ing to this basis c. Write down the basic feasible solution corresponding to the basis above, and its objective function value. d. Write down the values of the reduced cost...
Consider the following problem Minimize Z3x+2 subject to 3+26 and 20, 20 ()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. (c) Work through the simplex method step by step to solve the problem
Exercise 1. Please use the simplex method to solve the below LP min z=3.r - 12 s.t. 21; +12<8 21 +225 21 - 22 S4 21,220 a) Write the LP in standard form. b) Provide tableaus, BV, NBV, solution, objective value for each iteration of the simplex method. (Hint: the optimal value z=-5).
Exercise 1. Please use the simplex method to solve the below LP min z=3.r - 12 s.t. 21; +12<8 21 +225 21 - 22 S4 21,220 a) Write the LP in standard form. b) Provide tableaus, BV, NBV, solution, objective value for each iteration of the simplex method. (Hint: the optimal value z=-5).
Problem 2: (This is from Problems 4 and 5. Page 172 of the textbook) (a) Use Phase I Simplex Algorithm to find an initial basic feasible solution. Next, use the Simplex Tableau Method to solve this problem. Show that if ties are broken in favor of lower-numbered rows, then cycling occurs when the Simplex method is used to solve the following LP: max z-3x1 +x2 - 6x3 9x1 x2 -9x3 -2 x40 xi + (1/3)X2 - 2x3 - (1/3)X0 9x1...
(3) Kyle gave Cartman the tableau of a max-LP to solve using the simplex method. The LP had two variables (x1, 22) and two < constraints. Cartman decided to play a joke on Kyle, so he (a) changed the coefficient of zi in the first constraint from 6 to 9, and (b) solved the LP as a min-LP With these modifications, Cartman got the following"optimal" tableau after performing a single pivot. Find the correct optimal tableau that Kyle should have...
Exercise 1. Please use the simplex method to solve the below LP min 2=3.01 - 22 s.t. 2.c +228 2 + xy S5 21 - 22<4 2,220 a) Write the LP in standard form. b) Provide tableaus, BV, NBV, solution, objective value for each iteration of the simplex method. (Hint: the optimal value z=-5).
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