The Accommodation Decision

IBSS Annual Challenge 2014

Right-click to

continue

The academic year has just started…

…many, many students arrive in town…

Right-click to

continue

You want to find a nice place to live…… where will you settle?

IBSS Annual Challenge 2014

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

here?

here?

maybe here?

This is…

The Accommodation Decision!

Right-click to

continue

What do you have to do?Just choose a point (x,y)

on the map

IBSS Annual Challenge 2014

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

For example, you may choose point (3,1.8)

(3, 1.8)

Notice:• You can choose any x

between 0 and 10 and any y between 0 and 5

• They do NOT need to be integersRight-click

to continue

You want to live close to 3 important places:• The university (U),which is at coordinates () = (9,0)

• The supermarket (S),which is at coordinates (; ) = (0, 3)

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

IBSS Annual Challenge 2014

U (9,0)

S (0,3)

P (; )

• The “trendiest and most popular” place (P),

which is at coordinates(; )• The place where parties

will take place!• Location not known

(yet!): depends on the choices of all the students. How exactly?

(N is the number of students in town)

• x1, x2, etc. are the x choices of all students.

• y1, y2, etc. are the y choices of all students.

Right-click to

continue

Rental prices are regulated: you’ll pay the same rent everywhere in town…

Say there are only 3 students in town: Xavier (X), Yorick (Y) and Zoe (Z)

• X chooses location () = (3,1.8)

• And Z chooses (, ) = (8.16,2.34)

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

IBSS Annual Challenge 2014

U (9,0)

S (0,3)

P (; )=(4.35,1.9)

• Y chooses (, ) = (1.89,1.56)Thus: And

Right-click to

continue

So, P = (xP,yP) = (4.35,1.9)

Let us see how the trendy place P is determined with an example…

X (3,1.8)

Z (8.16,2.34)

Y (1.89,1.56)

..the more steps you take, the higher the cost (the more tired you get!):

• If you take h “horizontal” steps, the cost is

• So your total cost of going anywhere from home is

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

IBSS Annual Challenge 2014

U (9,0)

S (0,3)

• If you take v “vertical” steps, the cost is

Let’s go back to the example to see it more clearly, and

focus on Xavier’s situation…

Right-click to

continue

Now, when you walk from your home to any place, you suffer a cost…• “horizontal” steps

are taken in the East-West (or Left-Right) direction

• “vertical” steps are taken in the North-South (or Up-Down) direction

…and that the trendiest place was at point P=(4.35,1.9).

Now, let us compute Xavier’s cost of going to the University:• …and 1.8-0=1.8 vertical

steps…

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

IBSS Annual Challenge 2014

P(4.35,1.9)

• He will take 9-3=6 horizontal steps…So, Xavier’s cost of going to

the university is 36+1.62=37.62

Following a similar procedure, the cost of going to the supermarket S is 9.72

Remember that he chose location at point X=(3,1.8)…

• Remember that the cost formula is

• So the formula becomes

• So the formula becomes

𝒗=𝟏 .𝟖U (9,0)

𝒉=𝟔

• Cost of going to the university is 37.62

• Cost of going to the university is 37.62

• Cost of going to the supermarket is 9.72

…and the cost of going to the trendiest place P is 1.8275.

• Cost of going to the university is 37.62

• Cost of going to the supermarket is 9.72

• Cost of going to the trendiest place is 1.8275

Right-click to

continue

S (0,3)X (3,1.8)

• travel 48 times to/from the University (24 return trips),

• travel 12 times to/from the Supermarket (6 return trips)

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

IBSS Annual Challenge 2014

P

• and travel 30 times to/from parties at the trendiest place (15 return trips).

Your “Total Monthly Cost of Travelling” (TCMT) is the sum

of all of them.Thus, you want to choose a location

(x,y) that minimises your TCMTIt is the case that every month you will:

TMCT = =48*(cost of a trip to U)++12*(cost of a trip to S)++30*(cost of a trip to P)

𝒗=𝟏 .𝟖 U

𝒉=𝟔

The WINNER will be the person with the lowest TCMT.

Right-click to

continue

S(x,y)

• Xavier chose X=(3,1.8) and his costs are:

• Thus, TCMTX=48*37.62+ 12*9.72+30*1.8275 2,000

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

IBSS Annual Challenge 2014

P(4.35,1.9)

• Yorick chose Y=(1.89,1.56) and his TCMT is TCMTY 2,700

• Zoe chose Z=(8.16,2.34) and her TCMT is TCMTZ 1,400

Thus, in this case, Zoe is the WinnerLet’s see who the winner is

in the example…:Remember that: TMCT = =48*(cost of a trip to U)++12*(cost of a trip to S)++30*(cost of a trip to P)

U (9,0)

• TMCTX=2,000• TMCTX=2,000• TMCTY=2,700

Right-click to

continue

S (0,3)X (3,1.8)

• Cost of going to the university is 37.62

• Cost of going to the supermarket is 9.72

• Cost of going to the trendiest place is 1.8275

Y (1.89,1.56)

• TMCTX=2,000• TMCTY=2,700• TMCTZ=1,400

Z (8.16,2.34)

So email us your answer to: ibsschallenge@xjtlu.edu.cn

IBSS Annual Challenge 2014

And that’s it! Easy!

Right-click to

continue

Please include in your message:• Your forename(s) and your

surname• Your university, your

degree and your year of study

• Your club/association (if any)

And, most importantly,• Your choice of x• Your choice of y

You have time to submit your answer until next Friday 23 May at 23:59.

IBSS Annual Challenge 2014

So don’t be late! You can win awesome prizes, including 500RMB in cash!For more information, please go to http://academic.xjtlu.edu.cn/ibss/programmes (tab “IBSS Annual Challenge”)For questions: ibsschallenge@xjtlu.edu.cn Come and play!