Show that $(x_1,x_2,x_3)=(\frac{5}{26},\frac{5}{2},\frac{27}{26})$ is an optimal solution to the following LPP$,$ Please do not

use the simplex method.

$mamizez=9x_1+14x_2+7x_3$

subject $to2x_1+x_2+3x_{3}6$

$5x_1+4x_2+x_{3}12$

$2x_{2}5$

$x_1,x_2,x_3$ free

Hint: formulate the dual problem and find the feasible solution.