constraint

Examples of constraint in the following topics:

• Applications of Systems of Equations

  • Systems of equations can be used to solve many real-life problems in which multiple constraints are used on the same variables.
  • A system of equations can be used to solve a planning problem where there are multiple constraints to be taken into account:
  • There is a constraint limiting the total number of people in attendance to $56$, so:

• Application of Systems of Inequalities: Linear Programming

  • Linear programming involves finding an optimal solution for a linear equation, given a number of constraints.
  • Then, we can write two linear inequalities where three variables must be non-negative, and all constraints must be satisfied. 
  • Where $x=[x_{1}, x_{2},..., x_{n}]^{T}$ are the variables, $c=[c_{1}, c_{2},..., c_{n}]$ are the coefficients of the objective function, A is the left-side of the constraints, and $b=[b_{1}, b_{2},..., b_{p}]^{T}$ the right.
  • where the first row defines the objective function and the remaining rows specify the constraints.

• Applications and Mathematical Models

  • Systems of linear equations are common in science and mathematics, including Physics, Chemistry and maximization/minimization and constraint problems.

• Relative Minima and Maxima

  • Minima and maxima are used heavily in optimization problems and artificial intelligence where, given a number of constraints on resources, we want the best use of our resources.

• Integer Coefficients and the Rational Zeros Theorem

  • In algebra, the Rational Zero Theorem, or Rational Root Theorem, or Rational Root Test, states a constraint on rational solutions (also known as zeros, or roots) of the polynomial equation

• Fitting a Curve

  • Curve fitting is the process of constructing a curve, or mathematical function, that has the best fit to a series of data points, possibly subject to constraints.