The feasible region for a linear program is defined by these three constraints: $5$A $+5$B $<=400$; $-1$A $+1$B $<=10$; $1$A $+3$B $>=90$; A $>=0$; B $>=0.$ In this feasible region, the objective function $($A $$ B$)$ is maximized. Which of the following statements is true?

Group of answer choices

The feasible region has $4$ corner points all of which are equally good for this objective function.

The optimal objective value is $70.$

$(15,25)$ is the best corner point for this objective $.$

$(35,45)$ is the best corner point for $($A$-$B$)$