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 0.006
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.
a. Write the inequalities that describe her advertising needs.
b. Graph the region determined by these constraint inequalities.
c. Interpret the solution region in the context of this problem.
Chapter 8.1
2009 PBLPathways
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 0.006
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.
a. Write the inequalities that describe her advertising needs.
b. Graph the region determined by these constraint inequalities.
c. Interpret the solution region in the context of this problem.
2009 PBLPathways
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 0.006
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.
a. Write the inequalities that describe her advertising needs.
2009 PBLPathways
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 0.006
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.
a. Write the inequalities that describe her advertising needs.
x: number of minutes of television advertising
y: number of minutes of radio advertising
x0
y0
x  y  80
total amount of advertising
0.09 x reached
0.006 y  2.16
total number of people
2009 PBLPathways
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 0.006
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.
a. Write the inequalities that describe her advertising needs.
x: number of minutes of television advertising
y: number of minutes of radio advertising
x0
y0
x  y  80
0.09 x  0.006 y  2.16
2009 PBLPathways
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 0.006
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.
a. Write the inequalities that describe her advertising needs.
x: number of minutes of television advertising
y: number of minutes of radio advertising
x0
y0
x  y  80
total amount of advertising
0.09 x reached
0.006 y  2.16
total number of people
2009 PBLPathways
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 0.006
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.
a. Write the inequalities that describe her advertising needs.
x: number of minutes of television advertising
y: number of minutes of radio advertising
x0
y0
x  y  80
0.09 x reached
0.006 y  2.16
total number of people
2009 PBLPathways
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 0.006
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.
a. Write the inequalities that describe her advertising needs.
x: number of minutes of television advertising
y: number of minutes of radio advertising
x0
y0
x  y  80
0.09 x reached
0.006 y  2.16
total number of people
2009 PBLPathways
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 0.006
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.
a. Write the inequalities that describe her advertising needs.
x: number of minutes of television advertising
y: number of minutes of radio advertising
x0
y0
x  y  80
0.09 x reached
0.006 y  2.16
total number of people
2009 PBLPathways
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 0.006
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.
a. Write the inequalities that describe her advertising needs.
x: number of minutes of television advertising
y: number of minutes of radio advertising
x0
y0
x  y  80
0.09 x  0.006 y  2.16
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
0.09 x  0.006 y  2.16
x  y  80
x
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
0.09 x  0.006 y  2.16
x  y  80
x
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
0.09 x  0.006 y  2.16
x  y  80
(0, 0)
x
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
?
0  0  80
0.09 x  0.006 y  2.16
TRUE
0  80
x  y  80
(0, 0)
x
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
?
0  0  80
0.09 x  0.006 y  2.16
TRUE
0  80
x  y  80
(0, 0)
x
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
0.09 x  0.006 y  2.16
x  y  80
x
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
FALSE
0.09  0  0.006  0   2.16
0.09 x  0.006 y  2.16
x  y  80
x
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
0.09 x  0.006 y  2.16
x  y  80
x
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
0.09 x  0.006 y  2.16
x  y  80
x
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
0.09 x  0.006 y  2.16
x  0  80
x  80
x  y  80
x
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
0.09 x  0.006 y  2.16
x  0  80
x  80
x  y  80
x
(80, 0)
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
0.09 x  0.006 y  2.16
x  y  80
x
(80, 0)
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
0.09 x  0.006  0   2.16
0.09 x  0.006 y  2.16
0.09 x  2.16
x  24
x  y  80
x
(80, 0)
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
0.09 x  0.006  0   2.16
0.09 x  0.006 y  2.16
0.09 x  2.16
x  24
x  y  80
x
(24, 0)
(80, 0)
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
0.09 x  0.006 y  2.16
x  y  80
x
(24, 0)
(80, 0)
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
0.09 x  0.006 y  2.16
y  80  x
x
(24, 0)
(80, 0)
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
0.09 x  0.006 y  2.16
0.09 x  0.006  80  x   2.16
0.09 x  0.48  0.006 x  2.16
0.084 x  1.68
x  20
y  80  x
y  80  20  60
x
(24, 0)
(80, 0)
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
0.09 x  0.006 y  2.16
0.09 x  0.006  80  x   2.16
0.09 x  0.48  0.006 x  2.16
0.084 x  1.68
x  20
y  80  x
y  80  20  60
x
(24, 0)
(80, 0)
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
0.09 x  0.006 y  2.16
0.09 x  0.006  80  x   2.16
0.09 x  0.48  0.006 x  2.16
0.084 x  1.68
x  20
y  80  x
y  80  20  60
x
(24, 0)
(80, 0)
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
0.09 x  0.006 y  2.16
0.09 x  0.006  80  x   2.16
0.09 x  0.48  0.006 x  2.16
0.084 x  1.68
x  20
y  80  x
y  80  20  60
x
(24, 0)
(80, 0)
2009 PBLPathways
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 0.006
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.
b. Graph the region determined by these constraint inequalities.
y
0.09 x  0.006 y  2.16
(20, 60)
y  80  x
x
(24, 0)
(80, 0)
2009 PBLPathways
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 0.006
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.
c. Interpret the solution region in the context of this problem.
y
(20, 60)
x
(24, 0)
(80, 0)
2009 PBLPathways
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 0.006
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.
c. Interpret the solution region in the context of this problem.
y
(20, 60)
20 minutes of TV time
60 minutes of radio time
x
(24, 0)
(80, 0)
2009 PBLPathways
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 0.006
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.
c. Interpret the solution region in the context of this problem.
y
(20, 60)
40 minutes of TV time
20 minutes of radio time
x
(24, 0)
(80, 0)
2009 PBLPathways
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 0.006
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.
c. Interpret the solution region in the context of this problem.
y
(20, 60)
x
(24, 0)
(80, 0)
2009 PBLPathways