Constraint System Math Example 1

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Example 1

medium
Find all values of (x,y)(x, y) satisfying x+y=10x + y = 10, x≥0x \geq 0, and y≥0y \geq 0.

Solution

  1. 1
    From x+y=10x + y = 10: y=10−xy = 10 - x.
  2. 2
    Apply x≥0x \geq 0: this gives a lower bound on xx.
  3. 3
    Apply y≥0y \geq 0: 10−x≥010 - x \geq 0, so x≤10x \leq 10.
  4. 4
    The feasible set is all (x,10−x)(x, 10-x) with 0≤x≤100 \leq x \leq 10.

Answer

All (x,10−x)(x, 10-x) where 0≤x≤100 \leq x \leq 10.
A constraint system combines equations and inequalities that must all be satisfied simultaneously. The solution is the set of points meeting every constraint.

About Constraint System

A collection of equations and inequalities that must ALL be satisfied simultaneously by the same set of variable values.

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More Constraint System Examples

Example 2 hard

A shop sells notebooks for [formula]1. You have $12 and want at least 2 notebooks. How many pens can

Example 3 easy

List the integer solutions of [formula] with [formula] and [formula].

Example 4 medium

Is [formula] in the feasible region of [formula] and [formula]?

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