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FACILITY LOCATION

FACILITY LOCATION. AIM: To Locate A Facility Which Has Shortest Total Distance From Houses. STUDENT ASSIGNMENT. QUESTION

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FACILITY LOCATION

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  1. FACILITY LOCATION

  2. AIM: To Locate A Facility Which Has Shortest Total Distance From Houses.

  3. STUDENT ASSIGNMENT QUESTION 1.In the model, the only location we tried to find for the shelter that was not at one of the houses was the midpoint between the first and last house. How can we be sure that there is not another shelter location that would reduce the total distance travelled?

  4. ANSWER A— 150 m—B—75 m—C—75 m—D—50 m—E

  5. As we see in the graph, if we locate the shelter at C we will have the shortest distance travelled.

  6. QUESTION 2.Formulate a general rule telling where to locate the shelter so that the total distance travelled is shortest where there is an odd number of houses.

  7. ANSWER We can locate the shelter at the house, which is in the middle of the houses (C). Here it’s C.

  8. QUESTION 3.Will the rule that you developed in problem 2 be true if the houses are located so that six of them are closse together and the seventh one is far away?

  9. ANSWER House D is the middlest house of all. Also total distance travelled to reach shelter at D is the shortest of all.Thus we can say it obeys our rule.

  10. QUESTION 4. In the model, we considered what would happen with an odd number of houses. What would happen if there were an even number of houses on the block.

  11. ANSWER A—500 m—B—100 m—C—200 m—D—150 m—E—250 m—F

  12. If there are two houses; A—500 m—B Since there is one variety which is IABI, we can’t decide on the shortest distance.

  13. If there are four houses; A—300m—M—200m—B—100m—C—200m—D As we see in the table if we locate the shelter at B and C, distance travelled will be shortest.

  14. If there are six houses; A—500m—B—100m—C—200m—D—150m—E—250m—F As we see in the table if we locate the shelter at C and D, total distance travelled will be shortest.

  15. RULE: If we have even number of houses and if we want to make total distance shortest, we can locate the shelter at one of the middlest two houses. If we have 4 houses, we can locate it at second or third; if we have six houses we can locate it at third or fourth houses.

  16. PREPARED BY: ERDAL ERSOY

  17. THANS FOR LISTENING!

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