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

ByLuis

GabeSean

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

DataType 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

MaterialCost

2 1 2,500 MaterialCost

2 2.5 4,000 MaterialCost

3 1 3,600

ShippingCost

.75 1.25 1,500 ShippingCost

4 1 4,800 ShippingCost

.2 3 3,000

Plant in US                                 Plant in Thailand                     Plant in Mexico

US produced : $ 53 for A and $ 56 for BThailand produced: $45 for A and $50 for BMexico produced: $50 for A and $52 for B

MexicoTypes A B Capital $ ConstraintsLabor Cost .9 1 1,500 .9x+1y≤1500Material 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 = 3600-3x1000x

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

Type A B Capital $ ConstraintsLabor 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 ≤ 4800Total Capital 10300 x > 0 and y > 0

Y = 2000 – (3/4)x Y = 1600 – 0.8x Y = 4800 – 4x

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 StatesType 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

Y = 1333 – (2.5/3)x Y = 2500 – (2/1)x Y 1200 – (.75/1.25)x

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 $ ConstraintsLabor 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 ≤ 4800Total 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