Question $4$ options:

$($For T$/$F questions, enter T$$for True Statements$$and F$$for False Statements. If you do not follow the formatting, then your answer will be graded wrong. If your answer is correct, I will be able to manually change your grade for those questions later, but you will lose $25\%$ of the points. NO EXCEPTIONS, in order to be fair to everyone in the class.$)$

Any satisficing solution for a multi$-$objective optimization that keep one objective function as the objective, and then turns other ones to constraints $($upper limit for minimzation and lower limit for maximization$)$ will produce Pareto$-$efficient solutions. $(1$ point$)($T$/$F$?)$

In a class of $60$ students, we want to put them in $30$ groups of $2$ for the final projects. We ask each student to give a score of $5($most favorable$)$ to $1($least favorable$)$ to their classmates for how they like them to be their groupmates. Then we run a maximum assignment $($matching$)$ problem. The solution of this assignment problem will be binary, even if we do not enforce binary constraints. $(2$ points$)($T$/$F$?)$

In a class of $60$ students consisting of $20$ sophomores, $20$ juniors, and $20$ seniors, we want to put them in $20$ groups of $3$ for the final projects, where each group consists of one sophomore, one junior, and one senior student. We ask each student to give a score of $5($most favorable$)$ to $1($least favorable$)$ to their classmates for how they like them to be their groupmates. Then we run a maximum assignment $($matching$)$ problem. The solution of this assignment problem will be binary, even if we do not enforce binary constraints. $(2$ points$)($T$/$F$?)$