Exercise 5.2. Do not use MATLAB for this question. Consider the constraints 1 < 2rı + x2 < 4, 0 0. (a) Verify that the point r1 = r2 = 0 is not feasible. (b) Formulate a phase-1 LP with a single artificial variable. Define the phase-1 problem in such a way that you know an initial vertex for the phase-1 constraints in which 21 = x2 = 0. (c) Solve the phase-1 problem of part (b) using the simplex method for problems in all- inequality form. Give the value of the artificial variable at each iteration. (d) Use your phase-1 solution to define a feasible point for the original constraints. Is your solution a vertex for phase 2? Justify your answer.

An LP solution always provides a lower bound to an IP minimization problem: O True O False W

Exersise3: (a): Define the following terms: Management Science, Feasible region, Feasible Solution, Optimal Solution, Constraints, Extreme point, Objective function, Deterministic Model, Stochastic model and Sensitive analysis. (b): Find the Range of Optimality for c1 and c2 of the following LPP.     Max z =   5x1 + 10x2                                s.t.,          2x1 + 3x2    <   25                                               x1 +  2 x2     <   35                                     and  x1, x2  >

(9) Please answer correctly and fastly. Thanks