In the following problem, a minimization problem, the corresponding dual problem, and the final simplex tableau in the solution of the dual problem are given. Minimize C=15x, +36x, Maximize P=60y₁ +85y₂ 2y, +3y₂ ≤15 5y₁ +7y₂ ≤36 V₁.1₂ 20 subject to 2x₁ + 5x2 260 subject to 3x, +7x₂ 285 X₁, X₂ 20 a. Find the optimal solution of the dual problem Maximum of P= Y₁ = Y₂ = Y₁ Y2 X₁ X₂ P 01 520 3 1 0-7 30 3 00 5 10 1 435

Work through the simplex method (in algebraic form) step by step to solve the following problem. Maximize        Z = x1 + 2x2 + 2x3, subject to   5x1 + 2x2 + 3x3 ≤ 15                     x1 + 4x2 + 2x3 ≤ 12                      2x1+  x3 ≤   8 and x1 ≥ 0,    x2 ≥ 0,    x3 ≥ 0.

Solve the given linear programming problem using the table method. The table of basic solutions is provided. Maximize P= 15x, + 8x2 subject to X, + X2 56 Xq + 4x2 s 12 X1, X2 20 x1 S2 Feasible? Yes 6. 0. 12 No: Yes 6. -12 9. Yes No 12 4 -6 0. Yes

Use the Simplex method to solve this problem when a = 1. Hint: does the LPP have an optimal solution in this case?