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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

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