Problem 1 (10 marks)

Minimise:

Subject to:

f = 2x₁ - 6x₂ + 3x3 + 4x4 + 7x5 + 3x6 + 2x7

91 = x2 + 5x3 + 3x4 x5 + 2x6 + 3x7 ≥ 65

92 = -6x₁3x₂ − 2x3 + x4 + 2x5 - 2x6 ≥ -73

93-7x₁4x2 + 3x3

X₁, X₂ € (2,5,7,8), X3, X4 € {3,4,6}

X5, X6 ≥ 0, X7 ER

4x4 + 3x5 - 2x6 x7 ≤-66