Final Exam Review 1: Units A, B, and C Review

Front

What is the objective function in linear programming?

Back

An objective function is a mathematical expression that defines the goal of optimization, typically to maximize or minimize a quantity, such as profit or cost.

Front

How do you find the maximum value of an objective function given a feasible region?

Back

To find the maximum value, evaluate the objective function at each vertex of the feasible region and select the highest value.

Front

What does the absolute value of a number represent?

Back

The absolute value of a number represents its distance from zero on the number line, regardless of direction.

Front

How do you solve an absolute value equation?

Back

To solve an absolute value equation, set up two separate equations: one for the positive case and one for the negative case, then solve each equation.

Front

What is the transformation of the function g(x) = f(x-3) + 5?

Back

The function g(x) represents a horizontal shift to the right by 3 units and a vertical shift upward by 5 units from the original function f(x).

Front

What is a system of inequalities?

Back

A system of inequalities is a set of two or more inequalities with the same variables, which can be graphed to find a feasible region.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, graph each inequality as a line, then shade the appropriate region that satisfies all inequalities.

Front

What does the term 'feasible region' mean in linear programming?

Back

The feasible region is the set of all possible points that satisfy the constraints of a linear programming problem.

Front

What is the significance of the vertices in a feasible region?

Back

The vertices of a feasible region are significant because the maximum or minimum values of the objective function occur at these points.

Front

What is the meaning of 'no solution' in an absolute value equation?

Back

'No solution' means that there are no values of the variable that can satisfy the equation, often due to contradictory conditions.