Exercise 1.3. Phase I Simplex. In the first exercise, the initial tablea had a feasible solution when setting all the slack variables to the right hand side. This is not always the case. When that does not work, we must run the simplex method to find a feasible solution. Consider this problem Minimize Z=0.421 +0.5.22, subject to 0.3x1 + 0.1x2 6 and x1 > 0, 2220 We will augment the system with slack variables 81, 82, 83, 84 as Minimize subject to Z= 0.4x1 + 0.5x2 0.321 + 0.1x2 + $1 0.5x1 + 0.5x2 + S2 0.621 + 0.4.02 82 > 0, $3 > 0, 84 > 0. = 2.7 = 6 -33 + 84 = 6 and X1 > 0, x2 > 0, Si > 0, 1. Change the objective function to min 82 + 84. 2. Solve the new minimization problem using the simplex method. 3. Show that the resulting tableau holds a feasible solution to the original problem. 4. Explain why the resulting tableau has a feasible solution to the original