Production Planning

Reading the Dual: What Your LP Solution Is Really Telling You

By CashSheet Team··5 min read
Reading the Dual: What Your LP Solution Is Really Telling You

The hidden second answer

When you solve a linear program, you get two answers, not one. The first is obvious — the production mix that maximizes margin. The second is buried in the solver output, and it might be more useful: the dual values.

For every constraint in your LP, the solver computes a number called the dual (or shadow price). It tells you exactly how much your objective would improve if that constraint were relaxed by one unit. Most plants never look at it. They're leaving the most actionable insight in the solver on the table.

What a dual variable means

Imagine your LP includes a constraint: day-shift labor cannot exceed 60 hours. After the solve, the labor constraint has a dual value of $13.40. That number means: if you could buy one more hour of day-shift labor, your total margin would go up by $13.40. Buy two hours, get $26.80 more margin — until something else binds.

It's the marginal value of capacity, computed exactly, baked into the solve at no extra cost.

Why this is gold for decisions

Once you start reading duals, several common decisions get easier:

  • Overtime ROI. Overtime costs $22/hour. Day-shift labor's dual is $13.40. Don't run overtime; the math says it loses money.
  • Capacity expansion. The grind-capacity dual sits at $45/hour shift after shift. That's the strongest signal you'll ever get that a second grinder pays for itself.
  • Pricing on the margin. A customer wants 800 extra lb of Ribeye at the spot rate. The LP says it's feasible — but the dual on inventory tells you the exact displaced-margin cost. Now you can quote with a real floor, not a hunch.
  • Where to source. If raw-material constraint has a high dual at one facility and a low one at another, transfer. The dual difference is the upper bound on what the transfer is worth.

Where MakeSheet surfaces them

Every solve in MakeSheet returns a dual for every binding constraint. The capacity dashboard shows the live shadow prices for each resource — labor, grind, drop, freezer. When a sales rep clicks Check Availability, the response includes the dual on the binding constraint, so the rep can see not just "yes, we can promise it" but "and here's what it cost us in displaced margin."

The LP is good at finding the answer. Reading the dual is how you understand why that's the answer — and what to do next.

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