Maximize z = 2x1 +3x2 +x3 +4x4 Subject to x1 − x3 + x4 ≤ 5 −x1 +2x2 +x4 ≤6 x2 +2x3 +0.5x4 ≤8 xj≥0,j=...1, ,4 (a) Write the canonical form (or simplex form) of the LP model (call this iteration 0). (b) Perform two iterations (call these iterations 1 and 2) of the simplex algorithm. (c) What is the basic feasible solution you get from your last iteration (iteration 2)? Clarify basic variables and nonbasic variables. Also give the values of all the variables and the objective function. (d) Is the basic feasible solution you get from your last iteration (iteration 2) optimal? Why or why not?