Problem $8(10pts)$ Consider the following $LP$:

min,$2x_1+x_2$

$s.t.,5x_1+2x_2=10,$

$,x_1+4x_{2}4,$

$,x_1+x_{2}4,$

$,x_1,x_{2}0$

Use the Big$-M$ method solve the problem.

Table $2$: Food