Question

solve the following lp graphically: max z = 10x1 20x2 s.t. − x1 2x2 ≤ 15 x1 x2 ≤ 12 5x1 3x2 ≤ 45 x1, x2 ≥

Answer 1

To solve the given linear programming problem graphically, plot the feasible region and optimize the objective function by evaluating it at each corner point.

Step-by-step explanation:

To solve the given linear programming problem graphically, we need to plot the feasible region and optimize the objective function. Let's solve it step-by-step:

1. Plot the equations on the coordinate axes. The equations are:
   -x1 + 2x2 ≤ 15
   x1 + x2 ≤ 12
   5x1 + 3x2 ≤ 45
   x1, x2 ≥ 0
2. Find the feasible region which is the intersection of the shaded areas formed by the inequalities.
3. Plot the objective function z = 10x1 + 20x2 on the graph. Sketch the line with a positive slope.
4. Find the corner points of the feasible region where the objective function will be optimized.
5. Evaluate the objective function at each corner point and select the maximum value as the optimal solution.

By following these steps, you will be able to solve the given linear programming problem graphically.