For any tableau that requires using the simplex method algorithm to solve for optimal solutions, how does one find these optimal solutions in the RHS and the coefficients in the objective function wit...
For any tableau that requires using the simplex method algorithm to solve for optimal solutions, how does one find these optimal solutions in the RHS and the coefficients in the objective function without actually running the simplex method?
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For any tableau that requires using the simplex method algorithm to solve for optimal solutions, how does one find these optimal solutions in the RHS and the coefficients in the objective function wit...
We would like to answer the following question: How can we tell, using the Simplex Method,...
We would like to answer the following question: How can we tell, using the Simplex Method, that there is more than one optimal solution? To find out, let's use the simplex method on a problem from HW2 that we already know has multiple solutions. Maximizing 3x1 + 6r2 subject to the constraints 1 2 12 When you reach your final tableau, it should still be possible to pivot without changing the objection function row. How can you identify this phenomenon...
(2 marks) Solve (find the optimal point and objective function value at the optimal point) the...
(2 marks) Solve (find the optimal point and objective function value at the optimal point) the following optimisation problem min 2x+ y Subject to Obtain the gradient of both the objective function and constraint function at the optimal point. What condition do they meet at the optimal point? Suppose the right-hand side of the constraint equation is increased from 1 to 1.2. Without redoing the Lagrange multiplier method obtain an estimate for the change in objective function value. Verify using...
(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...
Solve the given linear programming problem using the simplex method. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY i...
Solve the given linear programming problem using the simplex method. If no optimal solution exists, indicate whether the feasible region is empty or the objective function is unbounded. (Enter EMPTY if the feasible region is empty and UNBOUNDED if the objective function is unbounded.) Minimize c = x + y + z + w subject to x + y ≥ 80 x + z ≥ 60 x + y − w ≤ 50 y + z − w ≤ 50...
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...
2. Consider the linear programm (a) Fill in the initial tableau below in order to start...
2. Consider the linear programm (a) Fill in the initial tableau below in order to start the Big-M Method tableau by performing one pivot operation. (6) The first tableau below is the tableau just before the optimal tableau, and the second one oorresponds to the optimal tableau. Fill in the missing entries for the second one. 1 7 56 M15 25 01 3/2 2 0 0 1/2 0 15/2 #310 0 5/2-1 o 1-1/2 0133/2 a1 a rhs (i) Exhibit...
1. (6 points) Find an optimal solution for the following transportation problem using the minimal...
1. (6 points) Find an optimal solution for the following transportation problem using the minimal cost method and the transportation algorithm: Minimize lahi + 2x12 + 2x13 + 4x21 + 3x22 + 4x23 + 4x31 + 1x32 + 3x33, subject to the constraints X11 + X12 + X13 = 100. x21 +x22 +x23 = 50. r31 + 232 +x33 100 x11 + 2'21 +2'3,-150. 12 22+32-50 x13 + x23 + x33-50. for all i, j = 1.2.3. xij > 0,...
Solve the system by using any method. If a system does not have one unique solution,...
Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. 4x + y = 16 x + y - 4 Part 1 Since the system has infinitely many solution(s), the equations are depende TTOO Part 2 out of 2 IA 2 The solution set is * is any real number} + XUO O In log
Decrease-by-Half Algorithm We can solve the same problem using a decrease-by-half algorithm. This...
Convert the pseudocode into a C++ function
Decrease-by-Half Algorithm We can solve the same problem using a decrease-by-half algorithm. This algorithm is based on the following ideas: In the base case, n 1 and the only possible solution is b 0, e 1 In the general case, divide V into a left and rnight half; then the maximum subarray can be in one of three places: o entirely in the left half; o entirely in the right half; or o...
Solve using the graphical method. Choose your variables, identify the objective function and the constraints, graph the...
Solve using the graphical method. Choose your variables, identify the objective function and the constraints, graph the constraints, shade the feasibility region, identify all corner points, and determine the solution that optimizes the objective function. Use this information to answer the following 8-part question: A small company manufactures two types of radios- regular and short-wave. The manufacturing of each radio requires two operations: Assembly and Finishing. The regular radios require 1 hour of Assembly and 3 hours of Finishing. The...
We would like to answer the following question: How can we tell, using the Simplex Method, that there is more than one optimal solution? To find out, let's use the simplex method on a problem from HW2 that we already know has multiple solutions. Maximizing 3x1 + 6r2 subject to the constraints 1 2 12 When you reach your final tableau, it should still be possible to pivot without changing the objection function row. How can you identify this phenomenon...
(2 marks) Solve (find the optimal point and objective function value at the optimal point) the following optimisation problem min 2x+ y Subject to Obtain the gradient of both the objective function and constraint function at the optimal point. What condition do they meet at the optimal point? Suppose the right-hand side of the constraint equation is increased from 1 to 1.2. Without redoing the Lagrange multiplier method obtain an estimate for the change in objective function value. Verify using...
(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...
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...
2. Consider the linear programm (a) Fill in the initial tableau below in order to start the Big-M Method tableau by performing one pivot operation. (6) The first tableau below is the tableau just before the optimal tableau, and the second one oorresponds to the optimal tableau. Fill in the missing entries for the second one. 1 7 56 M15 25 01 3/2 2 0 0 1/2 0 15/2 #310 0 5/2-1 o 1-1/2 0133/2 a1 a rhs (i) Exhibit...
1. (6 points) Find an optimal solution for the following transportation problem using the minimal cost method and the transportation algorithm: Minimize lahi + 2x12 + 2x13 + 4x21 + 3x22 + 4x23 + 4x31 + 1x32 + 3x33, subject to the constraints X11 + X12 + X13 = 100. x21 +x22 +x23 = 50. r31 + 232 +x33 100 x11 + 2'21 +2'3,-150. 12 22+32-50 x13 + x23 + x33-50. for all i, j = 1.2.3. xij > 0,...
Solve the system by using any method. If a system does not have one unique solution, state whether the system is inconsistent or whether the equations are dependent. 4x + y = 16 x + y - 4 Part 1 Since the system has infinitely many solution(s), the equations are depende TTOO Part 2 out of 2 IA 2 The solution set is * is any real number} + XUO O In log
Convert the pseudocode into a C++ function
Decrease-by-Half Algorithm We can solve the same problem using a decrease-by-half algorithm. This algorithm is based on the following ideas: In the base case, n 1 and the only possible solution is b 0, e 1 In the general case, divide V into a left and rnight half; then the maximum subarray can be in one of three places: o entirely in the left half; o entirely in the right half; or o...
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