Solve the following ILP using branch and bound techniques. Show complete and detailed solutions including graphs for each iteration. Use different colors of pen in graphing.
a. Objective Function
Max 7 = 7X1 + 9X2
Subject to
-X1 + 3X2 ≤ 6
7X1 + X2 ≤ 35
X1, X2 ≥ 0; and integers
b. Objective Function
Subject to
Min Z = - 5X1 - 4X2
X1 + X2 ≤ 5
10X1 +6X2 ≤45
X1,2 ≥ 0; and integers

### Graphical Analysis for Problem B
The graph shows the feasible region (shaded in yellow) for the linear constraints. The red dots represent the integer points within this region.

### Step 2: Evaluate the Objective Function at Integer Points
We now evaluate the objective function \( Z = -5X_1 - 4X_2 \) for each feasible integer point.It seems like I can’t do more advanced data analysis right now. Please try again later. If you have any specific questions or need further assistance, feel free to ask!

Learn how to solve Integer Linear Programming (ILP) problems using the branch and bound technique. This page includes detailed solutions and graphical analysis for two ILP problems: maximizing 7 = 7X1 + 9X2 subject to constraints, and minimizing Z = -5X1 - 4X2 subject to constraints. Explore step-by-step solutions and graphical representations for each iteration.

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