Maximize Z- 3x1 + 2x2 subject to constraints 2 x1 + x2 18 2x1+3x2=42 3 x1 + x2 ≥ 20 i. Prepare initial simplex table for the above LPP. ii. Also find entering vector and departing vector from this table.

max z = −40x1 − 30x2 − 20x3s.t.10x1 + 3x2 + 5x3 ≤ 104x1 + 10x2 + 4x3 ≤ 15x1, x2, x3 ≥ 0 .(i) State its dual problem, and find the optimal solution of the latter using the SimplexMethod.

Solve the following LP by using the dual simplex method:min 3x1 + 2x2 + 10s.t.3x1 + x2 ≥ 3,4x1 + 3x2 ≥ 6,x1 ≥ 1,x2 free.2

Use the simplex method to solve the (LP) model:maxZ = 5x_{1} + 4x_{2}Subject to6x_{1} + 4x_{2} <= 24 x_{1} + 2x_{2} <= 6 - x_{1} + x_{2} <= 1 x_{2} <= 2x_{1}, x_{2} >= 0

Convert the following LP into its dual form:min 3x1 − x2 + x3s.t.x1 − 2x2 − x3 ≤ 42x1 − x2 + x3 = 8x1 − x2 ≤ 6x1 ≥ 0; x2, x3 free

Write the dual of the following linear programming problem:Maximize 8x1 + 3x2 − 2x3subject to x1 − 6x2 + x3 > 25x1 + 7x2 − 2x3 = −4x1 ≤ 0, x2 ≥ 0, x3 unrestricted.