©Zarestky
Math 141 Quiz 5 Version B
10/8/2009
NAME:_________KEY_______________________________
1.
(5 pts) A concert tour plans to advertise upcoming tour dates and wants to maximize exposure time. The
advertising budget is $40,000 for both television and radio commercials. A radio commercial lasts 20
seconds and costs $250. A television commercial lasts 30 seconds and costs $600. There must be
between 40 and 64 radio commercials. The corresponding linear programming problem is formulated as
follows:
Let x = the number of radio commercials purchased
Let y = the number of television commercials purchased
Maximize Time T = 20x + 30y
subject to 250x + 600y ! 40000
40 ! x ! 64
y"0
A. What are the corner points of the solution region?
(40, 0), (64, 0), (40, 50), (64, 40)
B. What is the solution to the linear programming problem? Include the values of x and y. Be sure to
phrase your answer in the context of the problem.
Substitute the corner points into the objective function:
CP
(40, 0)
(64, 0)
(40, 50)
(64, 40)
T = 20x + 30y
800
1280
2300
2480
The maximum exposure time is 2480
seconds when 64 radio and 40 television
commercials are purchased.
For 2-7, consider the following sets:
U = {x | x is a lower-case letter in the English alphabet}
T = {x | x is a letter in the word triathlon}
B = {x | x is a letter in the word bicycle}
S = {s, w, i, m}
R = {r, u, n}
Mark each statement true or false. (1 pt each)
2.
TRUE FALSE
!" B
3.
S ! SC = U
4.
h! T "S
5.
T and R are disjoint.
6.
B! R = "
7.
n RC = 23
(
)
{ }
( )
TRUE FALSE
TRUE FALSE
TRUE FALSE
TRUE FALSE
TRUE FALSE