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İHSAN DOĞRAMACI FOUNDATION BİLKENT ERZURUM LABORATORY HIGH SCHOOL

İHSAN DOĞRAMACI FOUNDATION BİLKENT ERZURUM LABORATORY HIGH SCHOOL. Prepared by: Rabia HİZARCI. PACK THEM IN!. What is our problem?. Packing 175 cylindrical containers at minimum expense. All of the containers must be stored in an upright position. We have three different storage units:

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İHSAN DOĞRAMACI FOUNDATION BİLKENT ERZURUM LABORATORY HIGH SCHOOL

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  1. İHSAN DOĞRAMACI FOUNDATIONBİLKENT ERZURUM LABORATORY HIGH SCHOOL Prepared by: Rabia HİZARCI PACK THEM IN!

  2. What is our problem? • Packing 175 cylindrical containers at minimum expense.

  3. All of the containers must be stored in an upright position. • We have three different storage units: • 11 feet × 11 feet for $67 a month • 11 feet × 22 feet for $105 a month • 11 feet × 33 feet for $130 a month • All units are 10 feet high

  4. Let’s see our container! • r= 1¹ • h= 3¹

  5. Identical row alignment: • What happens if we pack the containers in this position?

  6. In order to find the number of containers per row, we divide 11, 22 and 33 by 2 respectively since the diameter of the base is 2. 11÷2 = 5 22÷2 = 11 33÷2 = 16

  7. We divide 11 feet by 2 in order to find the number of rows of containers. 11÷2 = 5 • Since the area is 10 feet high, we divide 10 by 3, which is the height of the containers, in order to find the number of layers. 10÷3 = 3

  8. So, from the data we have, we can make this chart: Unit Cost Number Rows Layers Total Units Cost for per row per row needed two months 11×11 $67 5 5 3 75 3 $402 11×22 $105 11 5 3 165 2 $420 11×33 $130 16 5 3 240 1 $260

  9. Staggered row alignment: • What happens if we pack the containers in this position?

  10. Before talking about this arrangement, let’s remember “pythagorean theorem” • a² + b² = c² √3 2 1 x + 1² = 2² x = √3

  11. In order to find the number of containers per row, we divide 11 feet and 33 feet by 2, but when we try to find it for 22 feet we first divide it by 2 and then substract 1 from it. • So; for11 feet = 5 containers per row 22 feet = 11(for odd numbered) 10 (for even numbered) containers per row 33 feet = 16 containers per row

  12. How do we find the number of rows? • First, we substract 2 from 11, then we divide our result by √3 and lastly we add 1. 11 - 2 = 9 9 ÷ √3 + 1 = 6 (actually the result is between 6 and 7)

  13. Since the area is 10 feet high, we divide 10 by 3, which is the height of the containers, in order to find the number of layers. 10÷3 = 3

  14. So, from the data we have, we can make this chart: Unit Cost Number Rows Layers Total Units Cost for per row per row needed two months $67 5 6 3 90 2 $268 $105 11 or 10 6 3 189 1 $210 $130 16 6 3 288 1 $260 11×11 11×22 11×33

  15. Student Assignment 1. From the information in your charts, what appears to be the leats expensive way to store the containers? • 11 feet × 22 feet of staggered row alignment is the best one. ($210)

  16. Would your decision be the same if the restriction of storing the containers in an upright position were removed? • If they were removed, we would be able to pack more containers in some of the units, but the answer would be same.

  17. What is the second-best choice? • Using the unit of 11 feet × 33 feet is the second best choice. ($ 260)

  18. THANKS FOR LISTENING!

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