10th Grade Optimization Quizzes

In 10th grade, optimization often progresses to linear programming. This involves finding the maximum or minimum value of a linear "objective function" that is subject to a set of constraints written as linear inequalities. The solution is found by graphing the feasible region and testing its vertices.

Start by having students graph systems of linear inequalities to identify the "feasible region." Explain the corner point principle: the maximum or minimum value of the objective function will always occur at one of the vertices of this region. Students then test the coordinates of each vertex in the objective function to find the optimal solution.

The best problems involve resource allocation. For example, a business wants to maximize profit by producing two different products, where each product requires a certain amount of time on two different machines with limited total hours available. These scenarios provide a clear context for setting up the objective function and constraints.

A frequent error is incorrectly graphing the inequality constraints or misidentifying the coordinates of the vertices, especially when a vertex is the intersection of two non-axial lines. Students may also forget to test all vertices to find the optimal value, or they may test points inside the region instead of only the corners.

These quizzes are available as both printable PDFs and interactive digital assignments on Wayground. You can use the printable version for focused, in-class practice and grade it with the Wayground for Teachers app, or assign the digital version as a self-grading quiz. Every quiz includes a complete answer key.

This topic directly supports high school standards for creating equations and inequalities to represent constraints, such as those in Common Core (A-CED.A.3). It provides a powerful, visual application for solving systems of inequalities and builds a conceptual foundation for more advanced optimization methods in later courses.