1. example 6
Advertising
A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Write the inequalities that describe her advertising needs.
Graph the region determined by these constraint inequalities.
Interpret the solution region in the context of this problem.
Chapter 8.1
2009 PBLPathways

2. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Write the inequalities that describe her advertising needs.
Graph the region determined by these constraint inequalities.
Interpret the solution region in the context of this problem.

3. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Write the inequalities that describe her advertising needs.

4. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Write the inequalities that describe her advertising needs.
x: number of minutes of television advertising
y: number of minutes of radio advertising
total amount of advertising
total number of people reached

5. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Write the inequalities that describe her advertising needs.
x: number of minutes of television advertising
y: number of minutes of radio advertising

6. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Write the inequalities that describe her advertising needs.
x: number of minutes of television advertising
y: number of minutes of radio advertising
total amount of advertising
total number of people reached

7. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Write the inequalities that describe her advertising needs.
x: number of minutes of television advertising
y: number of minutes of radio advertising
total number of people reached

8. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Write the inequalities that describe her advertising needs.
x: number of minutes of television advertising
y: number of minutes of radio advertising
total number of people reached

9. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Write the inequalities that describe her advertising needs.
x: number of minutes of television advertising
y: number of minutes of radio advertising
total number of people reached

10. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Write the inequalities that describe her advertising needs.
x: number of minutes of television advertising
y: number of minutes of radio advertising

11. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y

12. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y

13. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y
(0, 0)

14. Graph the region determined by these constraint inequalities.
A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y ?
TRUE
(0, 0)

15. Graph the region determined by these constraint inequalities.
A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y ?
TRUE
(0, 0)

16. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y

17. Graph the region determined by these constraint inequalities.
A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y
FALSE

18. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y

19. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y

20. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y

21. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y
(80, 0)

22. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y
(80, 0)

23. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y
(80, 0)

24. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y
(24, 0)
(80, 0)

25. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y
(24, 0)
(80, 0)

26. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y
(24, 0)
(80, 0)

27. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y
(24, 0)
(80, 0)

28. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y
(24, 0)
(80, 0)

29. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y
(24, 0)
(80, 0)

30. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y
(24, 0)
(80, 0)

31. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Graph the region determined by these constraint inequalities. x y
(20, 60)
(24, 0)
(80, 0)

32. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Interpret the solution region in the context of this problem. x y
(20, 60)
(24, 0)
(80, 0)

33. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Interpret the solution region in the context of this problem. x y
(20, 60)
20 minutes of TV time
60 minutes of radio time
(24, 0)
(80, 0)

34. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Interpret the solution region in the context of this problem. x y
40 minutes of TV time
20 minutes of radio time
(20, 60)
(24, 0)
(80, 0)

35. A candidate for mayor of a city wishes to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and each 1-minute spot on radio reaches million. The candidate feels that she must reach at least 2.16 million people, and she can buy a total of no more than 80 minutes of advertisement time.
Interpret the solution region in the context of this problem. x y
(20, 60)
(24, 0)
(80, 0)