Consider the following linear programming problem minimize subject to z= 1.01.01 - 22 - x1 + x2 > 0 – 21 – 12 > -3 $1.2 > 0 with (a) write the problem in standard form. (b) solve the problem in standard form graphically. also, • introduce appropriate slack or surplus variables and define the boundaries of the feasible region in your graphical representation. explain why slack variables are added and not subtracted from the left hand sides of the constraints. • indicate the shortest path to optimality. solve the problem manually using the simplex algorithm. determine the optimal solution x* and the optimal value z*. explain every step you make. in particular • how do you choose certain values to enter the basis? explain why. • how do you choose which variables should leave the basis? explain why. • how do you decide when to stop? explain why.