Consider the Linear Programming Problem $ P $: $$ \text{Minimize } 2x_1 - 5x_2 $$ subject to $$ 2x_1 + 3x_2 + s_1 = 12, $$ $$ -x_1 + x_2 + s_2 = 1, $$ $$ -x_1 + 2x_2 + s_3 = 3, $$ $$ x_1 \geq 0, x_2 \geq 0, s_1 \geq 0, s_2 \geq 0, \text{ and } s_3 \geq 0. $$ If $$ \left[ \begin{array}{c} x_1 \ s_1 \ s_2 \ s_3 \end{array} \right] $$ is a basic feasible solution of $ P $, then $ x_1 + s_1 + s_2 + s_3 = \underline{\hspace{1cm}}. $

Question

Consider the Linear Programming Problem $ P $: $$ \text{Minimize } 2x_1 - 5x_2 $$  subject to  $$ 2x_1 + 3x_2 + s_1 = 12, $$ $$ -x_1 + x_2 + s_2 = 1, $$ $$ -x_1 + 2x_2 + s_3 = 3, $$ $$ x_1 \geq 0, x_2 \geq 0, s_1 \geq 0, s_2 \geq 0, \text{ and } s_3 \geq 0. $$ If $$ \left[ \begin{array}{c} x_1 \ s_1 \ s_2 \ s_3 \end{array} \right] $$  is a basic feasible solution of $ P $, then $ x_1 + s_1 + s_2 + s_3 = \underline{\hspace{1cm}}. $

cdquestions Admin · Accepted Answer

Substitute the given basic feasible solution into the system of equations. Solving for the values of $ x_1, s_1, s_2, s_3 $ gives: $$ x_1 + s_1 + s_2 + s_3 = 5. $$ Thus, $ \boxed{5} $.

Show Hint

Correct Answer: 5

Solution and Explanation

Top Questions on Linear Programming

Questions Asked in GATE MA exam