Business I / Calculus of Variations
Practice question · Multiple choice

A firm ramps production from 0 to 1,000 units/day over 30 days. Adjusting quickly incurs high adjustment costs (x˙2\dot{x}^2 terms); staying below target loses revenue. What does the calculus of variations deliver here?

Hints
  1. The choice variable is the whole schedule x(t)x(t).
  2. The functional totals cost across the horizon.
Show the answer

C. The day-by-day ramp curve minimizing total cost

Why

The answer is a curve, typically a smooth ramp balancing adjustment cost against lost revenue at every instant, the balance being exactly what Euler–Lagrange enforces pointwise.

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