(See attached file for full problem description) --- This excercise shows that if we bring the dual problem into standard form and then apply the primal simplex method, the resulting algorithm is not identical to the dual simplex method... ---
Duality and complementary slackness
(See attached file for full problem description) --- Consider the linear program: (see attached) a) By inspection, argue that this problem cannot have an unbounded optimal solution. b) Convert... c) to g) in attachment ---
Finding the duals of the LP problem and finding basic solutions to the primal
(See attached file for full problem description)
Finding cost of optimal diet given the result from an LP solver
Please see attachment, and provide explanation if possible for the response to the questions
Consider a symmetric square matrix A and the following linear program: Min cx St Ax > c x > 0 Prove that if x* satisfies Ax* = c and x* > 0 then x* is an optimal solution to this linear program.
Consider the following algorithm for solving a linear program in standard form without having to use the Big-M method: Choose any basis. Check to see if this basis is primal feasible. If so, use this as your initial BFS and solve the problem with simplex. If the basis is primal infeasible, solve the problem using dual si ...continues
Specify whether the following statements are true or false and justify your answer. a) Suppose we have an optimal basic feasible solution for an LP in standard form. If we increase the cost of a non-basic variable xn, the current solution will always remain optimal. b) Suppose we have an optimal basic feasible solution for ...continues
Consider the following LP Min a + b + c + d St a + d = 3 b + d = 2 c + d = 0 a, b, c, d > 0 a) Write the dual of this problem. b) Given the primal basis {a, b, c}, construct the corresponding primal and dual solutions. c) What can you say about the optimality of this basis and its corresponding primal and d ...continues
(See attached file for full problem description with proper symbols) --- Consider the linear program: Min x + y St x + 2y = x, y > 0 a) Find (with any method you'd like) an optimal solution to this problem as a function of . b) Graph the optimal cost as a function of . c) Const ...continues
(See attached files for full problem description)
