P:\10th grade\capstone folder\snowboards r us

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P:\10th grade\capstone folder\snowboards r us

  1. 1. By Luis Gabe Sean Lopez
  2. 2. Problem <ul><li>They want to choose the best location, costs of materials and shipping arrangements by using linear programming. </li></ul><ul><li>To maximize profit </li></ul>
  3. 3. Three scenarios <ul><li>Mexico </li></ul><ul><li>Thailand </li></ul><ul><li>United States </li></ul>
  4. 4. Data Plant in US                                 Plant in Thailand                     Plant in Mexico US produced : $ 53 for A and $ 56 for B Thailand produced: $45 for A and $50 for B Mexico produced: $50 for A and $52 for B Type A B Capital Type A B Capital Type A B Capital Labor Cost 2.5 3 4,000 Labor Cost 1 .75 1,500 Labor Cost .9 1 1,500 Material Cost 2 1 2,500 Material Cost 2 2.5 4,000 Material Cost 3 1 3,600 Shipping Cost .75 1.25 1,500 Shipping Cost 4 1 4,800 Shipping Cost .2 3 3,000
  5. 5. Mexico Types A B Capital $ Constraints Labor Cost .9 1 1,500 .9x+1y≤1500 Material Cost 3 1 3,600 3x+1y ≤3600 Shipping cost .2 3 3,000 .2x+3y≤3000 Total Capital 8,100 x > 0 and y > 0
  6. 6. Calculations <ul><li>Example </li></ul><ul><li>.9x+1y≤1500 </li></ul><ul><li>1y = 1500 - .9 </li></ul><ul><li>Y = 1500 - .9 </li></ul><ul><li>3x+1y ≤3600 = </li></ul><ul><ul><li>y =3600 -3x </li></ul></ul><ul><li>.2x+3y≤3000 = </li></ul><ul><ul><li>y = 3600 – 3x </li></ul></ul>
  7. 8. Point of intersection <ul><li>Example </li></ul><ul><li>1000-(0.2/3)x = 1500 – 0.9x </li></ul><ul><li>.83x = 1000 = 1500 </li></ul><ul><li>.83x = 500 </li></ul><ul><li>= 602x </li></ul><ul><li>Substitute </li></ul><ul><li>1500-.9( 602 ) = 959 </li></ul><ul><li>(602,959) </li></ul><ul><li>1500-0.9x = 3600-3x </li></ul><ul><ul><li>1000x </li></ul></ul><ul><li>1500-.9(1000) = 60 </li></ul><ul><li>(1000,600) </li></ul>
  8. 9. Profit <ul><li>79968 – 8100 = -132 not profit </li></ul><ul><li>81200- 8100 = 1100 </li></ul><ul><li>Mexico produced: $50 for A and $52 for B </li></ul><ul><li>P = 50x + 52y </li></ul><ul><li>P = 50(602) + 50(959) = 79968 </li></ul><ul><li>P = 50(1000) + 52(600) = 81200 </li></ul>
  9. 10. Thailand <ul><li>Y = 2000 – (3/4)x </li></ul><ul><li>Y = 1600 – 0.8x </li></ul><ul><li>Y = 4800 – 4x </li></ul>Type A B Capital $ Constraints Labor Cost 1 .75 1,500 1 x + .75 y ≤ 1500 Material Cost 2 2.75 4,000 2 x + 2.5 y ≤ 4000 Shipping cost 4 1 4800 4 x + 1 y ≤ 4800 Total Capital 10300 x > 0 and y > 0
  10. 12. Points of intersection and profit <ul><li>1600 - .8x = 2000 – (3/4) </li></ul><ul><ul><li>754 = x </li></ul></ul><ul><li>1600 - .8(754) = 996 </li></ul><ul><li>(754,996) </li></ul><ul><li>2000 – (4/3)x = 4800-4x </li></ul><ul><ul><li>1096 </li></ul></ul><ul><li>2000 – (4/3) 9(1076 = 565 = y </li></ul><ul><li>(1096,565) </li></ul><ul><li>Thailand produced: $45 for A and $50 for B </li></ul><ul><li>P = 45x + 50y </li></ul><ul><li>P = 45(754) + 50(996) = 83730 </li></ul><ul><li>83730 – 10300 = 73430 </li></ul><ul><li>P = 45x + 50y </li></ul><ul><li>P = 45(1096) + 50(565) = 77570 </li></ul><ul><li>77570 – 10300 = 67270 </li></ul>
  11. 13. United States <ul><li>Y = 1333 – (2.5/3)x </li></ul><ul><li>Y = 2500 – (2/1)x </li></ul><ul><li>Y 1200 – (.75/1.25)x </li></ul>Type A B Capital $ Constraints Labor Cost 2.5 3 4,000 2.5x + 3y ≤4000 Material Cost 2 1 2,500 2x + 1y ≤ 2500 Shipping cost .75 1.25 1,500 .75x + 1.25y ≤1500 Total Capital 8,000 x > 0 and y > 0
  12. 15. Points of Intersection and profit <ul><li>1333 – (2.5/3)x = 2500 – (2/1)x </li></ul><ul><ul><li>1060 </li></ul></ul><ul><li>1333 – (2.5/3) (1060) = 449 </li></ul><ul><li>(1167,449) </li></ul><ul><li>1200-(.75/1.25)x = 1333-(2.5/3) </li></ul><ul><ul><li>578 </li></ul></ul><ul><li>S </li></ul><ul><li>1200-(.75/1.25)(578 = 853 </li></ul><ul><li>(278,853) </li></ul><ul><li>Profit </li></ul><ul><li>US produced : $ 53 for A and $ 56 for B </li></ul><ul><li>P = 53x + 56y </li></ul><ul><li>P = 53(1167) + 56(449) = 86995 </li></ul><ul><li>86995 – 8000 = 78995 profit </li></ul><ul><li>P = 53(578) + 56(853) = 78402 </li></ul><ul><li>78402 – 8000 = 70402 profit </li></ul>
  13. 16. Which one is the best? <ul><li>Thailand </li></ul>Type A B Capital $ Constraints Labor Cost 1 .75 1,500 1 x + .75 y ≤ 1500 Material Cost 2 2.75 4,000 2 x + 2.5 y ≤ 4000 Shipping cost 4 1 4800 4 x + 1 y ≤ 4800 Total Capital 10300 x > 0 and y > 0
  14. 17. Why? Thailand produced: $45 for A and $50 for B P = 45x + 50y Mexico > P = 50x + 52y US >P = 53x + 56y

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