HW_Ex_Ch5_QM - maximize Z = 25,000x1 18,000x2 31,000x3...

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MAT540 Chapter 5 Example Problems – QM for Windows Solution 5. (a) x1 = decanters, x2 = trays maximize Z = 50 x 1 + 10 x 2 subject to x 1 + x 2 ≤ 15 (glass, lbs) 4 x 1 + x 2 ≤ 25 (labor, hours) x 1, x 2 ≥ 0 and integer (b) x 1 = 6, x 2 = 1, Z = 310 1
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MAT540 Chapter 5 Example Problems – QM for Windows Solution 8. (a) x1 = condominium, x2 = land maximize Z = $8000 x 1 + 6000 x 2 subject to 70000 x 1 + 30000 x 2 ≤ 500000 1000 x 1 + 2000 x 2 ≤ 14000 x 1 ≥ 0 and integer x 2 ≥ 0 (b) x 1 = 5, x 2 = 4.5, Z = 67,000 2
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MAT540 Chapter 5 Example Problems – QM for Windows Solution 9. a). x1=lathe, x2= press, x3 = grinder maximize Z = 1,000x1 + 700x2 + 800x3 subject to $5,000x1 + 6,000x2 + 4,000x3 ≤ 10,000 (cost, $) x1, x2, x3 = 0 or 1 b). x1 = 1, x2 = 0, x3 = 1, Z = 1,800 3
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MAT540 Chapter 5 Example Problems – QM for Windows Solution 19. a). x1 = # of salespeople to East, x2 = # of salespeople to Midwest, x3 = # of salespeople to West
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Unformatted text preview: maximize Z = 25,000x1 + 18,000x2 + 31,000x3 subject to x1 + x2 + x3 = 100 Total salespersons 5,000x1 + 11,000x2 + 7,000x3 ≤ 700,000 Total expenses x1 ≥ 10 Minimum salespersons x2 ≥ 10 Minimum salespersons x3 ≥ 10 Minimum salespersons x1, x2, x3 ≥ 0 and integer b). Solution: x1 = 20, x2 = 10, x3 = 70, Z = 2,850,000 4 MAT540 Chapter 5 Example Problems – QM for Windows Solution 21. a) x1 = blush, x2 = white, x3 = red Maximize Z = 12,100x1 + 8,700x2 + 10,500x3 subject to: 360x1 + 375x2 + 410x3 ≤ 30,000 (grapes) x1 + x2 + x3 ≤ 67 (Storage) 14x1 + 10x2 + 18x3 ≤ 2,200 (production) x1/x3 ≥ 2 or x1 - 2x3 ≥ 0 (blush to red) x2/x1 ≥ 1.5 or x2 - 1.5x1 ≥ 0 (white to blush) x1, x2, x3 ≥ 0 and integer b) Integer solution: x1 = 22 x2 = 33 x3 = 11 Z = $668,800 5...
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