HLPL / VerTeX Modelling Language Documentation

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Your first variable

One decision, one number.

Chapter: I — Foundations · lesson id first-variable · practice lesson

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An optimization model decides values for variables. The simplest possible model has one variable x, no extra constraints, and an objective. Without bounds a maximisation can run away to infinity — so we bound x between 0 and 10 and ask the solver to maximise it.

var 0 <= x <= 10 declares the variable with its bounds attached inline — the cleanest way to say "x lives between 0 and 10". You'll see this inline-bound form throughout the rest of the course: var 0 <= x, var x <= 5, and var 0 <= x <= 1 are all valid. Variable bounds use only the <= operator — the lower bound goes on the left, the upper on the right.

Predict before running

Before you Run. Where will the solver place x?

• At the lower bound (0)
• Somewhere in the middle
• At the upper bound (10)

Starter code

model tiny
var 0 <= x <= 10
max x
end

import elytica
def main():
  elytica.init_model("tiny")
  elytica.run_model("tiny")
  print("x =", elytica.get_variable_value("tiny", "x"))
  return 0

Hint

Just run it. The solver pushes x to its upper bound.

What counts as correct

• no-error — Model solves
• numeric-match — Solver pushes x to its upper bound (10)
• code-contains — Reads variable values from the solver (no hardcoding)

Mastery variant

Same idea, different numbers. Bound the variable and minimise this time.

model tiny_v
var -4 <= w <= 7
min w
end

import elytica
def main():
  elytica.init_model("tiny_v")
  elytica.run_model("tiny_v")
  print("w =", elytica.get_variable_value("tiny_v", "w"))
  return 0

Read this through MCP: read with path: "lessons/first-variable", or resource hlpl://lessons/first-variable.