Formulate the following problem as a linear problem using the Big$-$M method.

$\{\begin{array}{ccc}\text{:}[& \text{M}\text{i}\text{n}\text{i}\text{m}\text{i}\text{z}\text{e}& ]\\ & \text{s}\text{u}\text{b}\text{j}\text{e}\text{c}\text{t}& to\text{:}\end{array}4x_1+3x_2+10y,1$