Mathematical Optimization

Purpose

Solve a two-variable linear program exactly by enumerating the vertices of the feasible region, and see which constraints bind and what an extra unit of each is worth.

Variables

• xlight reminders to send
• ynegotiations to hold
• c₁, c₂value of a reminder and of a negotiation
• r₁, r₂, r₃limits: team hours, negotiations, channel capacity

Assumptions

• Quantities are continuous and values and efforts are linear.
• A reminder takes 0.25 h and a negotiation 0.5 h.
• All parameters are synthetic.

Model

Data this would need in practice

• Real value and effort per action type.
• Real limits, including policy.
• Whether actions can be split or must be whole.

Interpretation

The optimum sits at a vertex. A binding constraint has a positive shadow price: the value gained per extra unit of its limit. A constraint that does not bind is worth nothing at the margin.

Limitations

• Real actions are discrete; integer solutions can differ.
• Linear values ignore diminishing returns.
• Two variables are a teaching case, not a production model.