Two television stations compete with each other, for viewing audience.
Local programming options for the 5:00 p.m. weekday time slot include
a sitcom rerun, an early news program, or a home improvement show.
Each station has the same programming options and must make its
preseason program selection before knowing what the other television
station will do. The viewing audience gains in thousands of viewers for
Station A are shown in the payoff table.
Station
B
Sitco
m
Rerun
b1
News
Progra
m
b2
Home
Improvem
ent
b3
Sitcom Rerun a1 10 –5 3
Statio
n A
News Program a2 8 7 6
Home
Improvement a3
4 8 7
Using the LP method, determine the optimal strategy for each station.
What is the value of the game? (28 points)
The Ranch House, Inc., operates five fast-food restaurants. Input measures
for the restaurants include weekly hours of operation, full-time equivalent
staff, and weekly supply expenses. Output measures of performance include
average weekly contribution to profit, market share, and annual growth rate.
Data for the input and output measures are shown in the following tables.
Input Measures
Restaurant Hours of
Operation
FTE Staff Supplies
($)
Bardstown 96 16 850
Clarksville 110 22 1400
Jeffersonville 100 18 1200
New Albany 125 25 1500
St. Matthews 120 24 1600
Output Measures
Restaurant Weekly Profit Market Share
(%)
Growth Rate
(%)
Bardstown $3800 25 8.0
Clarksville $4600 32 8.5
Jeffersonville $4400 35 8.0
New Albany $6500 30 10.0
St. Matthews $6000 28 9.0
a. Develop a linear programming model that can be used to evaluate the
performance of the Clarksville Ranch House restaurant. (7 points)
b. Solve the model. (7 points)
c. Is the Clarksville Ranch House restaurant relatively inefficient? Discuss.
(7 points)
d. Where does the composite restaurant have more output than the
Clarksville restaurant? How much less of each input resource does the
composite restaurant require when compared to the Clarksville restaurant?
(7 points) 1. Two television stations compete with each other, for viewing audience. Local programming options for the 5:00 p.m. weekday time slot include a sitcom rerun, an early news program, or a home improvement show. Each station has the same programming options and must make its preseason program selection before knowing what the other television station will do. The viewing audience gains in thousands of viewers for Station A are shown in the payoff table.
Using the LP method, determine the optimal strategy for each station. What is the value of the game? (28 points)
The Ranch House, Inc., operates five fast-food restaurants. Input measures for the restaurants include weekly hours of operation, full-time equivalent staff, and weekly supply expenses. Output measures of performance include average weekly contribution to profit, market share, and annual growth rate. Data for the input and output measures are shown in the following tables.
a. Develop a linear programming model that can be used to evaluate the performance of the Clarksville Ranch House restaurant. (7 points)
b. Solve the model. (7 points)
c. Is the Clarksville Ranch House restaurant relatively inefficient? Discuss. (7 points)
d. Where does the composite restaurant have more output than the Clarksville restaurant? How much less of each input resource does the composite restaurant require when compared to the Clarksville restaurant?
(7 points)