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

## on May 05, 2010

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## P:\10th grade\capstone folder\snowboards r usPresentation Transcript

• By Luis Gabe Sean Lopez
• Problem
• They want to choose the best location, costs of materials and shipping arrangements by using linear programming.
• To maximize profit
• Three scenarios
• Mexico
• Thailand
• United States
• 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
• 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
• Calculations
• Example
• .9x+1y≤1500
• 1y = 1500 - .9
• Y = 1500 - .9
• 3x+1y ≤3600 =
• y =3600 -3x
• .2x+3y≤3000 =
• y = 3600 – 3x
•
• 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)
• 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
• 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
•
• 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
• 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
•
• 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
• 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
• Why? Thailand produced: \$45 for A and \$50 for B P = 45x + 50y Mexico > P = 50x + 52y US >P = 53x + 56y