A simplex matrix is given. In this case the solution is complete, so identify the maximum value of f and a set of values of the variables that gives this maximum value. If multiple solutions may exist, indicate this and locate the next pivot. A) The maximum value of f is 160 when , and . B) The maximum value of f is 160 when , and . C) The maximum value of f is 160 when , and . D) The maximum value of f is 160 when , . Since multiple solutions are possible, pivot on 1 in R₄C_4. E) The maximum value of f is 160 when , . Since multiple solutions are possible, pivot on 2 in R₃C₅.

Question

Quizplus · Accepted Answer

The given simplex matrix has reached the complete solution, and the maximum value of f is 160 when x1 = 8, x2 = 4, and x3 = 0. This can be verified by observing that the pivot column is the one with the largest positive coefficient in the objective row (which is column 2 in this case), and the pivot row is the one with the minimum ratio of the right-hand side value to the coefficient of the pivot column (which is row 1 in this case). After performing the pivot operation, the resulting simplex matrix will have all non-negative entries in the bottom row (the objective row), indicating that the solution is optimal.

A Simplex Matrix Is Given