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The Accommodation Decision

The Accommodation Decision. Right-click to continue. IBSS Annual Challenge 2014. 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…. This is…. The Accommodation Decision!. … where will you settle?.

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The Accommodation Decision

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  1. The Accommodation Decision Right-click to continue IBSS Annual Challenge 2014

  2. The academic year has just started… …many, many students arrive in town… Right-click to continue

  3. You want to find a nice place to live… This is… The Accommodation Decision! … where will you settle? here? here? maybe here? Right-click to continue IBSS Annual Challenge 2014

  4. What do you have to do? For example, you may choose point (3,1.8) Just choose a point (x,y) on the map • Notice: • You can choose any x between 0 and 10 and any y between 0 and 5 • They do NOT need to be integers (3, 1.8) Right-click to continue IBSS Annual Challenge 2014

  5. (N is the number of students in town) • The “trendiest and most popular” place (P), • which is at coordinates(; ) • The university (U), • which is at coordinates () = (9,0) You want to live close to 3 important places: • The supermarket (S), • which is at coordinates (; ) = (0, 3) Rental prices are regulated: you’ll pay the same rent everywhere in town… • x1, x2, etc. are the x choices of all students. • y1, y2, etc. are the y choices of all students. • The place where parties will take place! • Location not known (yet!): depends on the choices of all the students. How exactly? S (0,3) P(; ) Right-click to continue U (9,0) IBSS Annual Challenge 2014

  6. Thus: And Let us see how the trendy place P is determined with an example… 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) • Y chooses (,) = (1.89,1.56) So, P = (xP,yP) = (4.35,1.9) S (0,3) X(3,1.8) P(; )= (4.35,1.9) Z(8.16,2.34) Y(1.89,1.56) Right-click to continue U (9,0) IBSS Annual Challenge 2014

  7. Let’s go back to the example to see it more clearly, and focus on Xavier’s situation… • So your total cost of going anywhere from home is • If you take v “vertical” steps, the cost is • If you take h “horizontal” steps, the cost is ..the more steps you take, the higher the cost (the more tired you get!): Now, when you walk from your home to any place, you suffer a cost… • “vertical” steps are taken in the North-South (or Up-Down) direction • “horizontal” steps are taken in the East-West (or Left-Right) direction S (0,3) Right-click to continue U (9,0) IBSS Annual Challenge 2014

  8. He will take 9-3=6 horizontal steps… Now, let us compute Xavier’s cost of going to the University: So, Xavier’s cost of going to the university is 36+1.62=37.62 …and that the trendiest place was at point P=(4.35,1.9). Remember that he chose location at point X=(3,1.8)… Following a similar procedure, the cost of going to the supermarket S is 9.72 …and the cost of going to the trendiest place P is 1.8275. • …and 1.8-0=1.8 vertical steps… • 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 • 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 • Remember that the cost formula is • So the formula becomes • So the formula becomes S (0,3) X(3,1.8) P(4.35,1.9) Right-click to continue U (9,0) IBSS Annual Challenge 2014

  9. Your “Total Monthly Cost of Travelling” (TCMT) is the sum of all of them. The WINNER will be the person with the lowest TCMT. • travel 12 times to/from the Supermarket (6 return trips) • and travel 30 times to/from parties at the trendiest place (15 return trips). Thus, you want to choose a location (x,y) that minimises your TCMT • travel 48 times to/from the University (24 return trips), It 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) S (x,y) P Right-click to continue U IBSS Annual Challenge 2014

  10. Thus, TCMTX=48*37.62+ 12*9.72+30*1.8275 2,000 • Zoe chose Z=(8.16,2.34) and her TCMT is TCMTZ1,400 • Yorick chose Y=(1.89,1.56) and his TCMT is TCMTY2,700 Thus, in this case, Zoe is the Winner • Xavier chose X=(3,1.8) and his costs are: Let’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) • 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 • TMCTX=2,000 • TMCTX=2,000 • TMCTY=2,700 • TMCTZ=1,400 • TMCTX=2,000 • TMCTY=2,700 S (0,3) X(3,1.8) P(4.35,1.9) Z(8.16,2.34) Y(1.89,1.56) Right-click to continue U (9,0) IBSS Annual Challenge 2014

  11. So email us your answer to: ibsschallenge@xjtlu.edu.cn And that’s it! Easy! • 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 Right-click to continue IBSS Annual Challenge 2014

  12. You have time to submit your answer until next Friday 23 May at 23:59. 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! IBSS Annual Challenge 2014

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