5.3-9. Consider the following problem. Minimize subject to Z=2x+3x2 + 2x3. x + 4x2 + 2x3 ≥8 + 2x2 + 2x, ≥6 3x and x2≥0. xz ≥ 0. Let x and x be the surplus variables for the first and second con- straints, respectively. Let xs and x, be the corresponding artificial variables. After you make the adjustments described in Sec. 4.6 for this model form when using the Big M method, the initial simplex tableau ready to apply the simplex method is as follows: Coefficient of: Basic Right Variable Eq. Z x1 x2 X3 XXXX Side N (0)-1-4M+2-6M+3 -2M+2 MOM 0-14M Xs (1) 0 1 4 2 -1100 8 X7 (2) 0 3 2 0 00-11 6 After you apply the simplex method, a portion of the final simplex tableau is as follows: Coefficient of: Basic Right Variable Eq. ZX1 X2 X3 X4 x5 X6 X7 Side Z (0) -1 M-0.5 M-0.5 X2 (1) 0 0.3 -0.1 X1 (2) 0 -0.2 0.4 (a) Based on the above tableaux, use the fundamental insight pre- sented in Sec. 5.3 to identify the missing numbers in the final simplex tableau. Show your calculations. (b) Examine the mathematical logic presented in Sec. 5.3 to vali- date the fundamental insight (see the T* = MT and t* = t + VT equations and the subsequent derivations of M and v). This logic assumes that the original model fits our standard form, whereas the current problem does not fit this form. Show how, with minor adjustments, this same logic applies to the current problem when t is row 0 and T is rows 1 and 2 in the initial simplex tableau given above. Derive M and v for this problem. (c) When you apply the t* =t+ VT equation, another option is to use t[2, 3, 2, 0, M, 0, M, 0], which is the preliminary row 0 before the algebraic elimination of the nonzero coeffi- cients of the initial basic variables x and x7. Repeat part (b) for this equation with this new t. After you derive the new v, show that this equation yields the same final row 0 for this problem as the equation derived in part (b). (d) Identify the defining equations of the CPF solution core- sponding to the optimal BF solution in the final simplex tableau.