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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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2. Ragsdale Page 40, Prob. 7

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3. Ragsdale Page 40, Prob. 8

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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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5. Ragsdale Page 40, Prob. 10

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6. Ragsdale Page 40, Prob. 11

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7. Ragsdale Page 40, Prob. 12

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8. ASWM Page 70, Problem 10, see lecture notes

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9. ASWM Page 70, Problem 11,

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10. ASWM Page 70, Problem 12,

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11. ASWM Page 70, Problem 13,

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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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