Linear Programming Review

Front

What is Linear Programming?

Back

Linear Programming is a mathematical method for determining a way to achieve the best outcome in a given mathematical model, often used for maximizing or minimizing a linear objective function subject to linear equality and inequality constraints.

Front

What is the feasible region in linear programming?

Back

The feasible region is the area on a graph where all the constraints of a linear programming problem overlap. It represents all possible solutions that satisfy the given inequalities.

Front

What type of line is used for inequalities with < or >?

Back

A dashed line is used for inequalities with < or > to indicate that the points on the line are not included in the solution set.

Front

What type of line is used for inequalities with ≤ or ≥?

Back

A solid line is used for inequalities with ≤ or ≥ to indicate that the points on the line are included in the solution set.

Front

How do you graph a system of inequalities?

Back

To graph a system of inequalities, first graph each inequality as if it were an equation (using solid or dashed lines as appropriate), then shade the area that satisfies each inequality. The overlapping shaded area represents the feasible region.

Front

What is an objective function in linear programming?

Back

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

Front

If the objective function is 30x + 50y, what does it represent?

Back

It represents a linear relationship where 'x' and 'y' are variables, and the coefficients (30 and 50) indicate the contribution of each variable to the total value being maximized or minimized.

Front

What does the corner point of the feasible region represent?

Back

The corner point of the feasible region represents a potential solution to the linear programming problem, where the objective function can be evaluated to find the maximum or minimum value.

Front

How do you determine the maximum profit from a corner point?

Back

To determine the maximum profit from a corner point, substitute the coordinates of the corner point into the objective function and calculate the resulting value.

Front

What inequalities represent Kate's jewelry selling situation?

Back

The inequalities are: 2x + 3y > 100 (to make at least $100) and x + y ≤ 40 (to limit the total pieces of jewelry to 40).