Consider the following LP: Maximize 3x + 5x2 + 2x3 + 3x4 subject to 2x +...

 

Transcribed Image Text:

Consider the following LP: Maximize 3x + 5x2 + 2x3 + 3x4 subject to 2x + 4x2 + 5x3 + 2x4 7 2x + 3x2 6 x + 4x2 4 3x3 + 4x4 2 12 x3 S 4 X4 3 *2. x3, x4 0. (a) Identify the easy constraints set (variable separable constraints). (b) Identify one extreme point of the easy constraint set. Write the Dantzig Wolfe's Restricted Master Problem (RMP) in standard form using the extreme point. (c) Solve the RMP using the revised simplex method. (d) Build the sub-problem using the dual variables of the RMP. Solve the sub-problem (maybe graphi- cally), and identify the entering column in RMP. (e) Add the entering column into the revised simplex tableau and identify the leaving variable. Update the revised simplex tableau. (f) Repeat Steps give in Part (d) & (e) until you hit optimal solution or unbounded direction. Consider the following LP: Maximize 3x + 5x2 + 2x3 + 3x4 subject to 2x + 4x2 + 5x3 + 2x4 7 2x + 3x2 6 x + 4x2 4 3x3 + 4x4 2 12 x3 S 4 X4 3 *2. x3, x4 0. (a) Identify the easy constraints set (variable separable constraints). (b) Identify one extreme point of the easy constraint set. Write the Dantzig Wolfe's Restricted Master Problem (RMP) in standard form using the extreme point. (c) Solve the RMP using the revised simplex method. (d) Build the sub-problem using the dual variables of the RMP. Solve the sub-problem (maybe graphi- cally), and identify the entering column in RMP. (e) Add the entering column into the revised simplex tableau and identify the leaving variable. Update the revised simplex tableau. (f) Repeat Steps give in Part (d) & (e) until you hit optimal solution or unbounded direction.