This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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okparaugochi2021, let's knock this out. Q.41) Slack variables are introduced into linear programming constraints to: A) Convert inequality constraints into equalities B) Increase the number of constraints C) Make the objective function non-linear D) Eliminate the need for non-negativity Step 1: Understand the purpose of slack variables. In linear programming, slack variables are non-negative variables added to "less than or equal to" () inequality constraints to transform them into equality constraints. This conversion is essential for applying methods like the simplex algorithm. Step 2: Evaluate the given options based on the definition. A) Convert inequality constraints into equalities: This is the primary function of slack variables. For example, x + y 10 becomes x + y + s_1 = 10, where s_1 0 is a slack variable. B) Increase the number of constraints: Slack variables increase the number of variables, not the number of constraints. Each inequality constraint is simply rewritten as an equality. C) Make the objective function non-linear: Slack variables are added to constraints, not the objective function, and they maintain the linearity of the problem. D) Eliminate the need for non-negativity: Slack variables themselves must be non-negative (s_i 0), and they do not remove the non-negativity requirements for the original decision variables. Step 3: Conclude the correct option. Based on the evaluation, option A accurately describes the purpose of introducing slack variables. The final answer is A Send me the next one 📸