Linear Programming

These problems require linear algebra experience. (See attached file for full problem description) --- 1. Find all basic solutions of the following system: -x1 + 2x2 + x3 + 3x4 - 2x5 = 4 x1 - 2x2 + 2x4 + x5 = 2 2. Find all extreme points of the following polyhedral set X = {(x1, x2, x3) : x1 - x2 + x3 ≤ 1, x1 -2x2 ≤ 4, x1, x2, x3 ≥ 0} Does X have any recession directions? Why? 3. Let X = {( x1, x2) : x1 - x2 ≤ 3, -x1 + 3x2 ≤ 3, x1 ≥ -3} Find all extreme points of X and represent x = (0,1) as a convex combination of extreme points. 4. Assumin... click for more

Project Management Critical path?

You are in the process of selecting and awarding a major contract as quickly as possible. Management has approved simultaneous advertisements in CBD (Commerce and Business Daily), over the internet and Global media (contract journals). Here are the activities for this project, constraints of each activity and the duration for each activity. 1. Requirements Development: 30 Days 2. Requirement Specification preparation: 40 Days (can be started at the same time as Activity 1: Requirements Development) 3. Management Approval: 5 Days (Only after completed Requirements Specification (Activity 2) has been submitted to them for review) 4. Advertise in CBD: 70 days (Must not start until Mana... click for more

Linear Programming

I am looking for a detailed solutions to these problems (solved step by step).Problems relate to Linear Programming.Solutions dont have to be typed,hand written are fine.

Simplex Tableau Linear Programming

(See attached file for full problem description)

Linear Programming Proof

I need the proof of the Linear programming problem attached. --- Consider the LP: Min ct x Subject to Ax ≥ b, x ≥ 0. One can convert the problem to an equivalent one with equality constraints by using slack variables. Suppose that the optimal basis for the equality constrained problem is B. Prove that w = cBB-1 ≥ 0. Where cB = coefficients of Basic variables. B-1 = Inverse of Basis matrix. (algebra of simplex method can be helpful in this proof) ---