Compare the LP relaxations of the three integer optimization problems:

$($Problem $1)$ max $14*$x$1+8*$x$2+6*$x$3+6*$x$4$

s$.$t$.28*$x$1+15*$x$2+13*$x$3+12*$x$4<=39$

x$1,$ x$2,$ x$3,$ x$4\backslash$in $\{0,1\}$

$($Problem $2)$ max $14*$x$1+8*$x$2+6*$x$3+6*$x$4$

s$.$t$.2*$x$1+$ x$2+$ x$3+$ x$4<=2$

x$1,$ x$2,$ x$3,$ x$4\backslash$in $\{0,1\}$

$($Problem $3)$ max $14*$x$1+8*$x$2+6*$x$3+6*$x$4$

s$.$t$.$ x$2+$ x$3+$ x$4<=2$

x$1+$ x$2<=1$

x$1+$ x$3<=1$

x$1+$ x$4<=1$

x$1,$ x$2,$ x$3,$ x$4\backslash$in $\{0,1\}$

Among these three problems, the LP relaxation of which problem can offer a solution whose objective value is closer to the optimal value of the corresponding integer optimization?

Group of answer choices

Problem $1$

Problem $3$

Problem $2$