A firm has prepared the following binary integer program to evaluate a number of potential new capital projects. The firm's goal is to maximize the net present value of their decision while not spending more than their currently available capital.

Max $100x_1+120x_2+90x_3+135x_4$

$s.t.150x_1+200x_2+225x_3+175x_{4}500\{$ Constraint $1\}$

$x_1+x_2+x_3+x_{4}2\{$ Constraint $2\}$

$x_2+x_{4}1\{$ Constraint $3\}$

$x_2+x_{3}1\{$ Constraint $4\}$

$x_1=x_4\{$ Constraint $5\}$

$x_j=\{\begin{array}{ccc}1,& if\text{p}\text{r}\text{o}\text{j}\text{e}\text{c}\text{t}jis\text{s}\text{e}\text{l}\text{e}\text{c}\text{t}\text{e}\text{d}& \end{array}$

$0,$ otherwise

Which of the constraints enforces a mutually exclusive relationship?

Constraint $5$

Constraint $3$

Constraint $2$

Constraint $1$

Constra$$nt $4$