Question

f) Now suppose that the only change in the onginal problem is that a new wariable has been introduced into the model as follows Maximize 3 4 2u subject to and Use duality theory to determine whether the previous optimal ion, along with хым о, is still optimal. (p) Use the fundamental insight presented in Se, 5.3 to identify the coefficients of as a nonbasic variable in the final set of equations resulting from the introduction of larw into the original model as shown in part(f).

Answer 1

Maximize z = 3x_1 + x_2 + 4x_3 + 2x_new subject to 6x_1 + 3x_2 + 5x_3 + 3x_new lessthanorequalto 25 3x_1 + 4x_2 + 5x_3 + 2x_new lessthanorequalto 20 and x_1 greaterthanorequalto 0, x_2 greaterthanorequalto 0, x_3 greaterthanorequalto 0, x_new greaterthanorequalto 0 By Duality Duel y Minimize W = 25 w_1 + 20 w_2 6 w_1 + 3 w_2 greaterthanorequalto 3 3 w_1 + 4 w_2 greaterthanorequalto 1 5 w_1 + 5 w_2 greaterthanorequalto 4 3 w_1 + 2 w_2 greaterthanorequalto 2 w_1, w_2 greaterthanorequalto 0 From first three inequality clearly minimum 6 w_1 + 3 w_2 = 3 gives 2 w_1 + w_2 = 1 5 w_1 + 5 w_2 = 4 gives w_1 + w_2 = 4/5 w_1 = 1/5, w_2 = 3/5 5 w_1 + 5 w_2 = 4