Operations Research: Why the Best Answer Sits in a Corner
The mathematics of better decisions: linear programs and the simplex method, duality and shadow prices, networks, integer and nonlinear models, dynamic programming and decisions under uncertainty.
Try 3 questions
1. What makes a model 'linear' in linear programming?
- Every term is a constant times one variable
- All the variables must take whole-number values
- Only a single constraint may be included at once
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Answer: Every term is a constant times one variable
Linearity means no products of variables, powers or other curves; each term is a constant times one variable.
2. The classic 'diet problem', one of the first tackled with linear programming, seeks what?
- The tastiest menu within a calorie limit
- The cheapest food mix meeting nutrient needs
- The fewest foods that fit a fixed budget
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Answer: The cheapest food mix meeting nutrient needs
It minimizes cost subject to minimum amounts of each nutrient, and its optimal diets were famously unappetizing.
3. Linear programming's divisibility assumption permits what kind of solution?
- Fractional values, like 2.5 units
- Only whole-number values
- Only values of zero or one
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Answer: Fractional values, like 2.5 units
LP lets variables take any real value; when only whole units make sense, integer programming is needed.
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