1: Consider the three-dimensional LP solution space in Figure below, whose feasible extreme points are A, B, . . . , J . All the constraints are of the type leq and all the variables x1, x2, and, x3 are nonnegative and for a certain objective function point H represents the optimal solution. (a) Propose a path that might be followed by the simplex algorithm to reach this optimal solution (b) How many constraints inequality did the LP problem have? and how are they represented? (c) Suppose that s1, s2, s3, and, s4( 0) are the slack variables associated with constraints represented by the planes CEIJF, BEIHG, DFJHG, andIHG. Identify the basic and nonbasic variables associated with the feasible solution points A, F , G and I. (d) If the objective function is to maximize z = x1 + 3x2 + 5x3 and going one iteration from the starting basic feasible point, what will be the nonbasic variable that will lead to the next simplex corner point? and what is the improvement in z associated with entering with that NB variable