Question

Find the optimal solution of the following linear programming

problem with the simplex method: Maximize Z = 5x1 + 15x2 subject to
3x1 + 4x2 <= 20 2x1 + 3x2 <= 40 and x1,x2 >= 0

Answer 1

To solve this linear programming problem using the simplex method, follow these steps: 1) Convert the problem into standard form. 2) Set up the initial simplex tableau. 3) Perform simplex iterations to find the optimal solution.

Step-by-step explanation:

To solve this linear programming problem using the simplex method, we need to convert the given problem into standard form.

1. Add slack variables to convert the inequalities into equations:
   3x1 + 4x2 + s1 = 20
   2x1 + 3x2 + s2 = 40
2. Add non-negativity constraints:
   x1, x2, s1, s2 >= 0

Next, we set up the initial simplex tableau and perform the simplex iterations to find the optimal solution. The optimal solution for this problem is x1 = 5, x2 = 0, with the maximum value of Z = 25.