NGPF 4.8 Constraints and Optimization

Front

What is the first step in solving systems with many constraints?

Back

List the constraints.

Front

Which set of inequalities corresponds to the graph that is shaded below the line and to the left of the y-axis?

Back

3x + 2y ≤ 15, x ≥ 1, y ≤ 3.

Front

Identify a point that falls within the shaded solution region on the graph where all the possible regions overlap.

Back

(4, 3).

Front

If a business aims to maximize profit instead of minimizing costs, what might change in their production strategy?

Back

The quantity of each product produced would change.

Front

What is the practice of finding the best of all possible solutions, which involves testing solutions in an equation to either maximize or minimize a certain parameter?

Back

Optimization.

Front

Define 'constraint' in the context of optimization problems.

Back

A constraint is a condition that must be met for a solution to be valid.

Front

What is the graphical representation of a system of inequalities called?

Back

Feasible region.

Front

Explain the term 'feasible solution' in optimization.

Back

A feasible solution is a solution that satisfies all constraints of the problem.

Front

What does it mean to 'eliminate redundant constraints'?

Back

It means removing constraints that do not affect the feasible region or solution.

Front

How does changing a constraint affect the feasible region?

Back

Changing a constraint can expand, shrink, or shift the feasible region.