Question

Solve the given linear programming problem below with graphical method.

MaxZ=3x1​+5x2​
x1​+2x2​≤6
2x1​+3x2​≤10
x1​≤22
x2​≥1
x1​,x2​≥0​

Answer 1

To solve the given linear programming problem with the graphical method, we need to graph the constraints, find the feasible region, and evaluate the objective function at the vertices. The vertex with the highest value of Z is the optimal solution.

Step-by-step explanation:

To solve the given linear programming problem using the graphical method, we need to graph the constraints and find the feasible region. Then, we evaluate the objective function at the vertices of the feasible region to find the maximum value of Z.

1. Graph the line x1 + 2x2 = 6. This line represents the constraint x1 + 2x2 ≤ 6.
2. Graph the line 2x1 + 3x2 = 10. This line represents the constraint 2x1 + 3x2 ≤ 10.
3. Graph the line x1 = 2. This line represents the constraint x1 ≤ 2.
4. Graph the line x2 = 1. This line represents the constraint x2 ≥ 1.
5. Shade the region that satisfies all the constraints. This is the feasible region.
6. Label the vertices of the feasible region.
7. Evaluate the objective function Z = 3x1 + 5x2 at each vertex of the feasible region.
8. Choose the vertex that gives the highest value of Z as the optimal solution.