The following problem description represents

Max $7x_1+3x_2$

subject $to$

$5x_1+7x_{2}27$

$4x_1+x_{2}14$

$3x_1-2x_{2}9$

$x_1,x_{2}0$

$x_1$ integer

a mixed$-$integer linear programming problem

a binary programming problem

a linear programming problem

a pure integer programming problem

a nonlinear programming problem