$[35$ points $+5$ bonus points$]$ Be prepared it is a long story. In the last class meeting of a

"BORING" course, you were informed that the second exam would include $4$ questions

out of the $6$ potential types of problems covered in this course. The night before the

exam, you had an unbelievable dream $($with a good night of sleep$),$ in which you

correctly guessed the four types questions of this exam, i$.$e$.,$ Shortest Path, CPM$,$ ILP,

Transportation.

In the morning, you confirmed the "RUMOR" that students are allowed to bring an $8x11$

cheat sheet $($one sided$).$ The area or space needed to write down the content in the cheat

sheet for each type of question can be found in the following Table. In addition, you have

another option, that is to memorize the content of any type of question. But to memorize,

it takes more time, which also can be found in the table. The expected scores for each

type by using the two different strategies are different and shown in the following table as

well.

To help understand the table better, for example, the "Shortest Path" column shows the

areas$/$spaces $(35i{n}^{{?}^{{?}^{?}}})$ needed to write it down on the cheat sheet, how much time it takes

to either write it down on cheat sheet or memorize it $($suppose you do not have enough

time to allow you do both$),$ the expected scores you will get by using the two different

strategies. Suppose you only use one strategy for each type of question.

Right before you start the preparation after you got up$,$ your roommate $($a$.$k$.$a$.,$ your best

friend$)$ throws a surprise party with no chance you can possibly resist. After the

"FANTASTIC" party, you only have $3$ hours to prepare. But you decide to use half an

hour to figure out your best preparation strategy, which you name it $"$B$-$R$-$F$".$ Please tell

us the rest of your story $($i$.$e$.,$ only need to formulate the optimization model $(35$

points$),$ you get $5$ bonus points if you figure out the right solution$).$