LINEAR PROGRAMMING 3.4 Learning goals represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret.

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LINEAR PROGRAMMING 3.4 Learning goals represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context

Vocabulary linear programming : identifies the minimum or maximum values of some quantity, given a set of constraints constraints : limits on the variables written as inequalities feasible region : graph of the system; contains all points that satisfies all the constraints objective function : the quantity to be maximized or minimized (often cost or profit); the process of minimizing or maximizing is called optimization

Ex 1 Graph and find the min and max.

Ex 2 Graph and find the min and max.

Ex 3 A furniture manufacturer can make from 30 to 60 tables a day and from 40 to 100 chairs a day. It can make at most 120 units in one day. The profit on a table is $150 and $65 on a chair. How many tables and chairs should they make to maximize their profit? How much is the maximum profit?