To find the maximum or minimum value of a function.

To solve systems of linear equations.

To determine the optimal allocation of resources.

To analyze the behavior of complex systems.

Differential Calculus

Integral Calculus

Linear Algebra

Probability Theory

A point where the function is continuous.

A point where the function is differentiable.

A point where the function has a maximum or minimum value.

A point where the function is equal to zero.

The first derivative of the function is equal to zero.

The second derivative of the function is positive.

The function is continuous at the critical point.

The function is differentiable at the critical point.

The second derivative of the function is positive.

The second derivative of the function is negative.

The function is continuous at the critical point.

The function is differentiable at the critical point.

A scatter plot

A line graph

A bar chart

A feasible region

The function that is being maximized or minimized.

The function that represents the constraints of the problem.

The function that represents the feasible region of the problem.

The function that represents the optimal solution of the problem.

An algorithm for solving linear programming problems.

A method for finding the feasible region of a linear programming problem.

A method for finding the optimal solution of a linear programming problem.

A method for finding the constraints of a linear programming problem.

A theorem that relates the primal and dual problems in linear programming.

A theorem that relates the feasible region of the primal and dual problems in linear programming.

A theorem that relates the optimal solution of the primal and dual problems in linear programming.

A theorem that relates the objective function of the primal and dual problems in linear programming.

A theorem that provides necessary and sufficient conditions for a point to be a local minimum or maximum of a convex function.

A theorem that provides necessary conditions for a point to be a local minimum or maximum of a convex function.

A theorem that provides sufficient conditions for a point to be a local minimum or maximum of a convex function.

A theorem that provides necessary and sufficient conditions for a point to be a global minimum or maximum of a convex function.

Convex optimization problems have a single global minimum, while non-convex optimization problems may have multiple local minima.

Convex optimization problems have a single global maximum, while non-convex optimization problems may have multiple local maxima.

Convex optimization problems have a unique optimal solution, while non-convex optimization problems may have multiple optimal solutions.

All of the above.

Stochastic Optimization

Deterministic Optimization

Linear Programming

Convex Optimization

A method for generating random samples from a probability distribution.

A method for solving linear programming problems.

A method for solving convex optimization problems.

A method for solving stochastic optimization problems.

Deterministic optimization problems have fixed parameters, while stochastic optimization problems have random parameters.

Deterministic optimization problems have a single optimal solution, while stochastic optimization problems may have multiple optimal solutions.

Deterministic optimization problems are easier to solve than stochastic optimization problems.

All of the above.

Minimizing the cost of a manufacturing process with uncertain demand.

Maximizing the profit of a portfolio with uncertain stock prices.

Scheduling a workforce with uncertain employee availability.

All of the above.