Problem 5.

Solving a BIP with one knapsack constraint Use branch-and-bound coupled with LP relaxation to solve the following binary integer program. Solve the LP relaxations by hand as shown in class. Be sure to draw the search tree and provide the relaxed LP solution and any other relevant information at each node. At each iteration, branch on the fractional variable in the relaxed solution and use a rounding technique to find feasible solutions.

Problem 4. Simplex method Work through the simplex method in both algebraic form and tableau form step by step to solve the following problem. Maximize Z =x1+2x2+4x3 subject to: 3xi+x2+5x3510 xi+4x2tx38 2xi+2x3s7 and X1,x2,x320 Problem 5. Solving a BIP with one knapsack constraint Use branch-and-bound coupled with LP relaxation to solve the following binary integer program. Solve the LP relaxations by hand as shown in class. Be sure to draw the search tree and provide the relaxed LP solution and any other relevant information at each node. At each iteration, branch on the fractional variable in the relaxed solution and use a rounding technique to find feasible solutions Max 3x +5x2 +8x, +x, +3x +10x 2+,+3, + +8k, s12 Problem 4. Simplex method Work through the simplex method in both algebraic form and tableau form step by step to solve the following problem. Maximize Z =x1+2x2+4x3 subject to: 3xi+x2+5x3510 xi+4x2tx38 2xi+2x3s7 and X1,x2,x320 Problem 5. Solving a BIP with one knapsack constraint Use branch-and-bound coupled with LP relaxation to solve the following binary integer program. Solve the LP relaxations by hand as shown in class. Be sure to draw the search tree and provide the relaxed LP solution and any other relevant information at each node. At each iteration, branch on the fractional variable in the relaxed solution and use a rounding technique to find feasible solutions Max 3x +5x2 +8x, +x, +3x +10x 2+,+3, + +8k, s12