hw lp2 lp graphics: solutions. most of the problems...
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HW LP2 LP Graphics: Solutions. Most of the problems are from Chapter 2 of Ragsdale Text.
1. Ragsdale Page 40, Prob. 6
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4. Ragsdale Page 40, Prob. 9
X1
X2
0 5 10 15 20 25
5
10
15
20
(0, 15) obj = 300
(0, 12) obj = 240
(6.67, 5.33) obj =140
(11.67, 3.33) obj = 125(optimal solution)
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12. Ragsdale Page 41, Prob. 13, Chapter 2
X1 = # of TV spots, X2 = # of magazine ads
MAX 15 X1 + 25 X2 (profit)
ST 5 X1 + 2 X2 < 100 (ad budget)
5 X1 + 0 X2 ≤ 70 (TV limit)
0 X1 + 2 X2 ≤ 50 (magazine limit)
X1, X2 ≥ 0
Note: OBJ. could be $0.05 x 300,000 TV + $0.05 x 500,000 Mag or
Max: $15,000TV + 25,000Mag
S.T.
5,000TV + 2000Mag <=100,000
5,000TV <= 70,000
2,000Mag <= 50,000
TV, Mag >= 0
Once 1,000 is used to divided each term, the result should be the same.
X1
(14,15)
X2
10
20 10
20
30
40
(14,0)
(0,25) (10,25)
15X1+25X2=400
15X1+25X2=775
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13. Ragsdale Page 41, Prob. 14
X1 = tons of ore purchased from mine 1, X2 = tons of ore purchased from mine 2
MIN 90 X1 + 120 X2 (cost)
ST 0.2 X1 + 0.3 X2 > 8 (copper)
0.2 X1 + 0.25 X2 > 6 (zinc)
0.15 X1 + 0.1 X2 > 5 (magnesium)
X1, X2 ≥ 0
Copper Zinc Mag Cost
Ore 1 20% 20% 15% $90
Ore 2 30% 25% 10% $120
Needed 8 6 5
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