CALCULATORS / DESIGN TRADEOFFS AND OPTIMIZATION

Constraint-feasibility explorer calculator

Intersection of two scalar bound intervals; no general constraint solver.

optimization-constraint-feasibility.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenario	lowermm	uppermm	widthmm
	3	5	2
	4	5	1

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

nonempty intersection2.00 mm✓ passes

BASELINE INPUTS

lowerA1 mmupperA5 mmlowerB3 mmupperB8 mm

CALCULATED

lower3 mm

upper5 mm

width2 mm

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Constraint-feasibility explorer
# Scope: Intersection of two scalar bound intervals; no general constraint solver.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

lowerA = 1 mm
upperA = 5 mm
lowerB = 3 mm
upperB = 8 mm

lower := max(lowerA,lowerB) [mm]
upper := min(upperA,upperB) [mm]
width := upper-lower [mm]

check nonempty intersection: width >= 0 mm

scenario alternative: lowerB = 4 mm

Calculated from your source · not saved

Baseline · Baseline

nonempty intersection2.00 mm ✓ passes

alternative · alternative

nonempty intersection1.00 mm ✓ passes

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

lower: lower = max(lowerA,lowerB) [mm]
upper: upper = min(upperA,upperB) [mm]
width: width = upper-lower [mm]

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

lower a: 1 mm
upper a: 5 mm
lower b: 3 mm
upper b: 8 mm

Calculated

lower: 3 mm
upper: 5 mm
width: 2 mm

Assumptions and limits

Intersection of two scalar bound intervals; no general constraint solver.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Constraint-feasibility explorer. Inputs: variables; bounds; engineering constraints. Outputs: feasible combinations; active constraints. Model scope: Objectives, bounded variables and explicit constraints. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

Inputs: variables, bounds, engineering constraints
Outputs: feasible combinations, active constraints
Modes: calculate, compare, sweep
Drawing: Tradeoff and Pareto plots

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS