Lesson 8: 1-8 Optimization with Linear Programming

1. Tell which inequality symbol would correspond to each of the following phrases: more than, no more than, at least, no less than.
2. What are some ways you can make sure your graphs are accurate?

Linear Programming
Feasible Region
Bounded
Unbounded
Optimize

A.CED.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

SAT questions related to slope: 8-3-13, 6-3-1, 5-4-7, 8-3-19, 7-4-17, 1-3-6, 3-4-8; systems: 4-3-16, 1-3-18, 1-3-9, 2-3-2, 8-3-18, 6-4-11, 7-3-3, 1-3-11, 7-4-11, 1-4-19, 8-3-10, 2-4-29, 2-3-20, 3-3-9; writing equations: 5-4-11, 4-3-8, 8-4-7, 1-3-12, 7-3-19; inequalities: 5-4-13, 7-4-5, 4-4-19, 8-3-6, 1-4-28, 5-3-7, 6-3-14; graphing: 6-3-5; total unit: 2-3-9

The process of finding maximum or minimum values of a function for a region defined by linear inequalities is called linear programming.

An electronics company produces two types of smart phone docking stations. If at least 2000 items must be produced per shift, how many of each type should be made to minimize costs? The company is experiencing limitations, or constraints, on production caused by customer demand, shipping, and the productivity of their factory. A system of inequalities can be used to represent these constraints.

When using linear programming to solve real-world problems, it is important for students to follow the seven steps. Encourage students to show their work and label each step as they work through the problem.

Students may need to be reminded that neither the maximum nor minimum automatically occurs at the smallest/largest (x,y) coordinate. The max/min depend on the f(x,y) function in the situation.

Have students use different colored pencils to shade the different regions of a graph defined by the inequalities in a linear programming problem. This should help students clarify the relationship between the various regions in these graphs.

McGraw Hill resources

McGraw Hill resources