Question

$\text{Consider the primal problem in LP.}$

$\text{Maximize Z}=4X_1+3X_2$

$\text{Subject to}$

$X_1+X_2\le 82X_1+X_2\le 10X_1;X_2\ge 0$

$\text{together with its dual (LD) Then}$

• A. LP and LD both are infeasible
• B. LP is feasible but LD is infeasible
• C. LP and LD both are feasible
• D. LP is infeasible but LD is feasible

Answer 1

The correct option is C LP and LD both are feasible

$Z_{max}=4X_1+3X_2$

$\text{Statements :}$

$X_1+X_2\le 8$

$2X_1+X_2\le 10$

$X_1;X_2\ge 0$

$\frac{X_1}{8}+\frac{X_2}{8}\le 1$

$\frac{X_1}{5}+\frac{X_2}{10}\le 1$


Primal problem has feasible solution space. Hence an optimal solution exists for primal. If primal is feasible, dual is also feasible.