Combining constraints into a single graph

Question

Question 1: For each of the following constraints, draw a separate graph to show the non-negative solutions that satisfy this constraint.

1. x₁ + 3x₂ ≤ 6

2. 4x₁ + 3x₂ ≤ 12

3. 4x₁ + x₂ ≤ 8

4. Combine these constraints into a single graph to show the feasible region for the entire set of functional constraints plus non-negativity constraints.

Question 2: Given the following objective function for a linear programming model

maxZ = 2x₁ + 3x₂

1. Draw a graph that shows the corresponding objective function lines for Z = 6, Z = 12, and Z = 18.

2. Find the slope-intercept form of the equation for each of these three objective functions lines. Use a table to compare the slopes and the intercepts for these three lines e.g., Slope-intercept form Slope Intercept

• Z = 6
• Z = 12
• Z = 18