p:\10th grade\capstone folder\snowboards r us
TRANSCRIPT
Problem
They want to choose the best location, costs of materials and shipping arrangements by using linear programming.
To maximize profit
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