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

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Transcript

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