Question

We would like to answer the following question: How can we tell, using the Simplex Method, that there is more than one optimal solution? To find out, let's use the simplex method on a problem from HW2 that we already know has multiple solutions. Maximizing 3x1 + 6r2 subject to the constraints 1 2 12 When you reach your final tableau, it should still be possible to pivot without changing the objection function row. How can you identify this phenomenon from the numbers in the final tableau?

Answer 1

Given collect from the data let us assume that the equations we have consider that the equations are Now take the equations max: 3x_1 + 6x_2 s.t to the constrains (1 1 1 2 1 8) x lessthanorequalto (4 3 12) and x greaterthanorequalto 0 Now x_1 + 2x_2 lessthanorequalto 4 x_1 + x_2 lessthanorequalto 3 x_1 + 8x_2 lessthanorequalto 12, x_i greaterthanorequalto 0. Now its stock variables are s_1 s_2 s_3 let max z = 3x_1 + 6x_2 s. t x_1 + 2x_2 + s_1 = 4 x_1 + x_2 + s_2 = 3 x_1 + 8x_2 + s_3 = 12 then x_i greaterthanorequalto 0, s_i greaterthanorequalto 0 \r\n it is the most of -ve values are \r\n we have to taken from the table-3 should be optimal solutions are x_1 = 4/3, x_2 = 4/3, and z = 12 let These are the external optimal solutions are x_1 = 2, x_2 = 1, z = 12 These