Given the following linear programming problem with two non-negative variables $\left(X_{1}\right.$ and $\left.X_{2}\right), 3$ constraints (all $\leq$ type), and a maximize objective function $\left(Y_{i}\right.$, where $i=1,2,3$, respective to the dual variables associated with constraints 1,2 and 3),
Max: $250 X_{1}+500 X_{2}$
Constraints: $X_{1} \leq 320 \quad 2 X_{1}+5 X_{2} \leq 1100 \quad 1 X_{1}+1.2 X_{2} \leq 480$
Variables are non-negative one of the constraints of the dual problem is
A) $0 Y_{1}+2 Y_{2}+1.2 Y_{3} \geq 320$
B) $1 Y_{1}+2 Y_{2}+1 Y_{3} \geq 500$
C) $0 Y_{1}+5 Y_{2}+1.2 Y_{3} \geq 500$
D) $0 Y_{1}+5 Y_{2}+1.2 Y_{3} \geq 480$

Question

Quizplus · Accepted Answer

The dual problem of a linear programming problem involves converting the maximization problem into a minimization problem, where the coefficients of the objective function become the right-hand side values of the constraints, and the coefficients of the constraints become the coefficients in the dual constraints. For each variable $X_i$ in the primal, there is a corresponding constraint in the dual. The coefficients in the primal constraints for $X_2$ are 0, 5, and 1.2 for the three constraints, respectively. These become the coefficients in one of the dual constraints. Since the objective function coefficient for $X_2$ is 500, the corresponding dual constraint for $X_2$ is $0Y_1 + 5Y_2 + 1.2Y_3 \geq 500$, matching option C.

Given the Following Linear Programming Problem with Two Non-Negative Variables (X1\left(X_{1}\right.(X1​

Given the Following Linear Programming Problem with Two Non-Negative Variables $\left(X_{1}\right.$