For linear programming techniques to yield mathematically valid outcomes________________?
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Answer: C. A. or B.
Explanation
Linear programming models rely strictly on linear mathematical relationships between variables. Both the objective function and all constraints must be linear, meaning either positive or negative. Therefore, relations between factors must be linear in either a positive or negative sense. Linear equations graph as straight lines on a Cartesian coordinate system plane. The simplex algorithm solves these linear constraint equations to find optimal resource allocations. Non-linear relationships violate core mathematical assumptions required for standard LP solutions.
Operations researchers use linear programming to optimize supply chains and production schedules. Verifying linearity ensures that optimization algorithms converge on valid mathematical solutions. Business decision-making relies on these models to maximize profit while minimizing operational costs. Option A is incomplete because negative linear relationships are also mathematically valid. Option B is incomplete because positive linear relationships are equally valid in models. Option D describes experimental control rather than the mathematical requirement of linearity.
- Subject
- Engineering
- Category
- Mechanical Engineering
- Topic
- —
- Difficulty
- medium
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