Ali is still deciding upon which courses to take by defining binary decision variables X$1,$ X$2,...,$ X$6$ for them and putting in an optimization model.

$($Note that:

I want your models to be linear.

Also, the question is going to be graded automatically. Therefore, I give you options for the blanks and your solution must be chosen from the options. Make sure that you type the exact choices $($not the choice number$)$ per blank. No spaces, quotation marks, or anything extra. For instance, if it is choice a$)+,$ you enter $"+"($without the quotation marks obviously$).$

Consider each part independently. Also, each part is graded separately.

You must fill all the blanks for the formula to be fully correct.

Questions are graded automatically. 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.$)$

A$.$ If Ali wants to take $4,$ they cannot undertake more than one of $1,2,3.$

X$1$

$+$

X$2$

$+$

X$3$

$>=$

$1$

$*$

$1$

$*$

X$4$

Choices for the first blank: a$)+$ b$)-$ c$)*$ d$)/$

Choices for the second blank: a$)+$ b$)-$ c$)*$ d$)/$

Choices for the third blank: a$)>=$ b$)<=$ c$)=$ d$)>$ e$)<$

Choices for the fourth blank: a$)-1$ b$)0$ c$)0\mathrm{.}5$ d$)1$ e$)2$ f$)3$ g$)4$

Choices for the fifth blank: a$)+$ b$)-$ c$)*$ d$)/$

Choices for the sixth blank: a$)0$ b$)0\mathrm{.}5$ c$)1$ d$)2$ e$)3$ f$)4$

Choices for the seventh blank: a$)+$ b$)-$ c$)*$ d$)/$

B$.$ Ali is deciding whether or not get a double major. That decision is denoted by binary decision variable D$1,$ where $1$ means going for a double major and $0$ means otherwise. If they go for it$,$ they must collect $10$ points. They would collect n points for taking any Xn for advance classes, i$.$e$.,$ n $=4,5,6.($In other words, they'd collect $4$ points for taking X$4,5$ for taking X$5,$ and $6$ for taking X$6.)$