$1.)$ Imagine that you are responsible for scheduling speakers at a conference. You have $5$

speakers and $4$ total talks. A speaker can speak more than once $($so long as the talks do not

overlap$),$ and it is not necessary $($or possible$)$ to schedule every available speaker $(5$ speakers

into $4$ talks$).$ Each talk is assigned a room and time$-$slot; a speaker must have enough content

to fill the entire talk $($if they have more than enough, assume they can cut it down to appropriate

length$)$ and must have the right media for that room's display options $($see below$).$ Assume each

talk will only have one speaker assigned at any given time.

The talks are: Talk $1$: Room $100,9$:$00$am$-9$:$30$am

Talk $2$: Room $200,9$:$00$am$-10$:$00$am

Talk $3$: Room $100,9$:$30$am$-10$:$30$am

Talk $4$: Room $300,9$:$00$am $-10$:$30$am

The rooms have the following equipment$/$capabilities: Room $100$: Mac w$/$ Keynote, $($NO internet;

just to be clear, if it's not listed, it's not available$)$ Room $200$: Microsoft PC w$/$ Office, DVD$,$

Internet Connection Room $300$: Microsoft PC w$/$ Office, Mac w$/$ Keynote, DVD$,$ Internet

Connection

The speakers have the following presentations info:

Speaker $1$: $90$ mins, Youtube videos and web$-$pages Speaker $2$: $40$ mins, PowerPoint w$/$

Youtube videos Speaker $3$: $120$ mins, Keynote Presentation Speaker $4$: $35$ mins, PowerPoint

Presentation Speaker $5$: $70$ mins, DVD and Youtube videos

Now, answer the following questions to formulate the problem as a constraint satisfaction

problem $($CSP$).$ HINT: Your constraints should say which talks can or can't occur at the same

time; domains should show who can speak at that talk.

a$.$ State the variables:

b$.$ State the constraints $($be formal in your constraint definitions and use implicit constraints$)$:

c$.$ State the domains for each variable:

d$.$ Given your results for the domains in $($c$),$ answer the following questions:

I. Which speaker$($s$)$ is the most useful to the conference organizer? Why?

II$.$ Which speaker$($s$)$ is the least useful to the conference organizer? Why?

III. Given the MRV method, which talk$($s$)$ would you attempt to schedule first?

IV$.$ Is it possible to schedule all the talks? If YES, then give a valid assignment of speakers to

talks. If NO$,$ then state why not.

e$.$ Draw the constraint graph for this problem $($based on your answers to $($b$))$: