A linear programming problem has been formulated as follows:

Maximize $10x_1+20x_2$

$x_1+2x_{2}100$

$2x_1+x_{2}100$

$x_{1}0,x_{2}0$

Which of the following represents the optimal solution to this problem?

$x_1=50,x_2=50$

$x_1=50,x_2=0$

$x_1=50,x_2=10$

$x_1=100,x_2=50$

$x_1=0,x_2=50$