Consider the following linear programming problem: Maximize 40 X1 + 30 X2 + 60X3
Subject to: X1 + X2 + X3 ≥ 90
12 X1 + 8 X2 + 10 X3 ≤ 1500
X1 , X2 , X3 ≥ 0
How many slack, surplus, and artificial variables would be necessary if the simplex were used to solve this problem?
A)3 slack, 3 surplus, and 3 artificial
B)1 slack, 2 surplus, and 2 artificial
C)1 slack, 4 surplus, and 4 artificial
D)1 slack, 1 surplus, and 1 artificial

Question

Quizplus · Accepted Answer

In the given linear programming problem, the simplex method would require 1 slack variable for the '≤' inequality (to convert it into an equation), no surplus variables since there are no '≥' inequalities that need to be converted into equations, and 1 artificial variable for the '≥' inequality to convert it into an equation and ensure feasibility in the initial simplex tableau.

Consider the Following Linear Programming Problem: Maximize 40 X1