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

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Definitions:

Spark Plugs

A device for delivering electric current from an ignition system to the combustion chamber of a spark-ignition engine to ignite the compressed fuel/air mixture.

Air-Fuel Mixture

The blend of air and fuel that is fed into an internal combustion engine's cylinders for combustion.

Combustion Chamber

The enclosed space within an engine where fuel combustion occurs, driving the pistons and producing power.

Ignite

To set alight or begin to burn; in automotive terms, refers to the initiation of combustion.