You Have Formulated a Problem with Three Constraints: (1) 2X₁ $\le$

question 32

Multiple Choice

You have formulated a problem with three constraints: (1) 2X₁ + 3X₂ + 4X₃ $\le$ 300; (2) X₁ + X₂ $\ge$ 40; (3) X₁ + X₂ + X₃ = 100.Which of the following states that at least 2 of these 3 constraints must hold? (M = a large value)

• A)2X₁ + 3X₂ + 4X₃ - MY₁ \(\le\) 300
• X₁ + X₂ - MY₂ \(\ge\)40
• X₁ + X₂ + X₃ - MY₃ = 100
• Y₁ + Y₂ + Y₃ \(\ge\)2
• B)2X₁ + 3X₂ + 4X₃ - MY₁ \(\le\) 300
• X₁ + X₂ - MY₂ \(\ge\) 40
• X₁ + X₂ + X₃ + MY₃ \(\ge\) 100
• Y₁ + Y₂ + Y₃ \(\ge\) 2
• C)2X₁ + 3X₂ + 4X₃ - MY₁ \(\le\) 300
• X₁ + X₂ + MY₂ \(\ge\) 40
• X₁ + X₂ + X₃ - MY₃ \(\le\) 100
• X₁ + X₂ + X₃ + MY₃ \(\ge\)100
• Y₁ + Y₂ + Y₃ \(\le\) 1
• D)2X₁ + 3X₂ + 4X₃ - MY₁ \(\le\)300
• X₁ + X₂ – MY₂\(\ge\) 40
• X₁ + X₂ + X₃ – MY₃ \(\le\) 100
• Y₁ + Y₂ + Y₃\(\le\) 1