a.
To write: The system of inequalities.
Given:
A regular doghouse requires 7 hours to build and 3 hours to paint.
A deluxe doghouse requires 11 hours to build and 4 hours to paint.
The company employs 5 builders and 2 painters.
Each employee can work a maximum of 40 hours.
Calculation:
Let
Since there are 5 builders and each can work for a maximum of 40 hours, therefore the total building hours available is
Since there are 2 painters and each can work for a maximum of 40 hours, therefore the total painting hours available is
The number of hours required to build
Therefore, the building hour’s inequality is
The number of hours required to paint
Therefore, the painting hour’s inequality is
Since the number of doghouses cannot be negative, therefore
Hence, the system of inequalities is,
b.
To graph: Solution set of the system of inequalities in part (a).
Given:
Calculation:
The graph of the system of inequalities is,
The shaded region is the solution set of the system of inequalities.
c.
To find: the number of doghouses must be built, painted to maximize sales.
Approximately 18 deluxe doghouses must be built and painted to maximize the sales.
Given:
A regular doghouse can be sold for $100, and the deluxe doghouse can be sold for $200.
Calculation:
The amount received from selling
The corner points of the solution set are
Now at
At
At
Clearly, the maximum sales is $3636.4 and it occurs at the point
Hence, approximately 18 deluxe doghouses must be built and painted to maximize the sales.
Chapter 14 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