Consider the following linear programming model: Maximize subject to x1 + 2x2 x1-2x24 -X1+22 4 -x1 + x21 x10, x2 0 a) Augment the above model b) How many basic variables will there be in a basic feasible solution to the augmented model? How many non-basic variables will there be? Make sure to show your (simple) calculation. c) For the augmented model, suppose the slack variables are the basic variables and the other variables are the non-basic variables of an initial basic feasible solution. Construct the initial table for the simple method. d) Beginning with this initial table (constructed in Part c) solve the augmented model using the Simplex method in tabular form. At each iteration: . Clearly define the basic feasible solution and the objective function value State whether the solution is optimum or not If not optimum, determine the entering variable and the leaving variable (if it exists) State the row operations made to move from one table to the next At termination, state whether there is a unique optimum, alternative optima, or unboundedness NOTE: Use a table with the following format to perform your Simplex operations. Basic Equation Z X1 X2 Xk RHS Ratio Variable Number Z (0) Xi (1) Xj (2) B