✓ Lesson Check
Do you know HOW?
Graph each system of inequalities.
Graph each system of constraints. Then name the vertices of the feasible region.
Do you UNDERSTAND?
- Vocabulary Explain why the inequalities of a linear programming problem are called constraints. Hint: Use the definition of constraint as part of your answer.
- Compare and Contrast What are some similarities between solving a linear programming problem and solving a system of linear inequalities? What are some differences?
- Open-Ended Write a system of constraints whose graphs determine a trapezoid. Write an objective function and evaluate it at each vertex.
Practice and Problem-Solving Exercises
A Practice
See Problem 1.
Graph each system of constraints. Name all vertices. Then find the values of x and y that maximize or minimize the objective function.
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Maximum for N = 100x + 40y
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Minimum for C = x + 3y
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Maximum for P = 3x + 2y
See Problem 2.
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Air Quality A city wants to plant maple and spruce trees to absorb carbon dioxide. It has $2100 to spend on planting spruce and maple trees. The city has
Spruce and Maple Tree Data Spruce Maple Planting Cost $30 $40 Area Required Carbon Dioxide Absorption 650 lb/yr 300 lb/yr SOURCE: Auburn University and Anderson Associates
- Use the data from the table. Write the constraints for the situation.
- Write the objective function.
- Graph the feasible region and find the vertices.
- How many of each tree should the city plant to maximize carbon dioxide absorption?
Table of Contents
- 5-1 Polynomial Functions
- 5-2 Polynomials, Linear Factors, and Zeros
- 5-3 Solving Polynomial Equations
- 5-4 Dividing Polynomials
- 5-5 Theorems About Roots of Polynomial Equations
- 5-6 The Fundamental Theorem of Algebra
- 5-7 The Binomial Theorem
- 5-8 Polynomial Models in the Real World
- 5-9 Transforming Polynomial Functions