Practice question · Sort into groups
Ordinary optimization or calculus of variations? Sort each problem by the object being chosen.
Groups: Choose a number · Choose a path (function)
- The single price that maximizes this month’s profit
- How fast to extract an oil field over 20 years
- A 30-year consumption-savings plan maximizing lifetime utility
- The production ramp-up schedule minimizing total cost
- The order quantity minimizing inventory cost
Hints
- Ask what the answer is: a number, or a whole path?
- Anything optimised over a horizon points to the second.
Show the answer
Choose a number: The single price that maximizes this month’s profit, The order quantity minimizing inventory cost
Choose a path (function): A 30-year consumption-savings plan maximizing lifetime utility, The production ramp-up schedule minimizing total cost, How fast to extract an oil field over 20 years
Why
If the answer is a value, ordinary calculus; if the answer is a curve through time, variations. The tell: does the problem say "over" a horizon?
Practise Calculus of Variations
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