CC Math 3Name:______

Unit 2A- Linear Relationships REVIEW

Fill in the blank:

  1. In a linear programming problem:
  1. The shaded region is called the ______region.
  2. The function that is to be maximized or minimized is the ______function.
  3. If there is a maximum or minimum, it will occur at the ______of the shaded region.
  4. The set of inequalities that represents the limitations on the resources is the set of ______.

2. Find the values ofxandythat maximize the objective functionP= 3x+2yfor the graph. What is the maximum value?

3. Given the system of constraints, name all vertices. Then find the maximum value of the given objective function.

Maximum for

Use the information below to answer questions 4-8.
As a receptionist for a hospital, one of Elizabeth’s tasks is to schedule appointments.
She allots 60 minutes for the first visit and 30 minutes for a follow-up.
The doctor cannot perform more than seven follow-ups per day.
The hospital has eight hours available for appointments. The first visit costs $120 and the follow-up costs $70.
Let x be the number of first visit and y be the number of follow-ups.

4. Write a system of inequalities to represent the number of first visits and the number of follow-ups that can be performed.

5. Graph the system of inequalities showing the feasible region to represent the number of first visits and the number of follow-ups that can be performed.
6. List the coordinates of the vertices of the feasible region to represent the number of first visits and the number of follow-ups that can be performed.
7. Determine the number of first visits and follow-ups to be scheduled to make the maximum income.
8. What is the maximum income that the doctor receives per day?

9. Write the system of inequalities that best represents this graph?

10. The VBC Company makes two models of office chairs. The company’s profit is $15 on each Model Q chair and $20 on each model R chair. To use linear programming to maximize profit, the company’s finance officer developed this feasible region from the constraints on the company’s resources and the pattern of demand for its products. The number of Model Q chairs to be made each week is represented byxandyrepresents the number of Model R chairs to be made each week. How many of each model should the company make each week in order to maximize profit?

11. Solve the system of inequalities by graphing.

x> 1
y> 8

12. Graph the solution ofand

13. Which system of equations is shown?

14. What is the solution of the system shown in this graph?

15. Solve the system:

16. How would you CLASSIFY this system

17. What are the vertices (intersection points) of the feasible region for the constraints:

18. On a feasible region whose vertices are (2,10), (3,7), (5,6) (6,4), what is the minimum of the objective function R=6x-4y, and where does it occur?

19. What is the 30th term of the sequence? 7,16,25,34,…….

20. Which arithmetic sequence includes the term 27?

A. B. C.

21. Which arithmetic sequence does NOT include the term 33? 7,16,25,34,…….

For 22-23: A) Decide whether each formula is explicit or recursive.

AND B) Then find the first five terms of each sequence.

22.

23.