To State:
What are the unknowns in the given situation.
What are the constraints due to each given condition.
If there are any implicit constraints.
The number of samples of Type II Bacteria that should be used to minimize the cost.
The number of samples used of Type I (say
There are implicit constraints
The minimum cost is
Given:
Each sample of Type I bacteria produces four new viable bacteria.
Each sample of Type II bacteria produces three new viable bacteria.
At least
The number of type I samples must be at least
A sample of type I costs
Concepts Used:
Modelling a situation as a Linear Programming Problem (LPP).
Solving a LPP graphically.
Calculations:
Summarize the given information in a table:
Type I Sample | Type II Sample | Total | |
Number | |||
New Viable Bacteria | |||
Cost |
Write the constraints:
Write the objective function: the cost
Determine the feasible region by graphing the constraint inequalities. Also determine the corner points of the feasible region.
Evaluate the objective function
The minimum cost is
Conclusion:
The minimum cost is
Chapter 3 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education