1. Even though
independent gasoline stations have been having a difficult time, Susan Solomon
has been thinking about starting her own independent gas station. Susans problem is to decide how large her
station should be. The annual returns
will depend on both the size of the station and a number of marketing factors
related to oil industry and demand for gasoline. After careful analysis, Susan developed the
following table:
Sizes of Gasoline Station
Good Market
($)
Fair Market
($)
Poor Market
($)
Small
$70,000
$30,000
-$30,000
Medium
$110,000
$50,000
-$40,000
Large
$170,000
$70,000
-$50,000
1.
Develop a decision table for this
decision.
2.
What is the Maximax decision?
3.
What is the Maximin decision?
4.
What is the criterion of realism decision?
5. Develop
an Opportunity Loss Table
6.
What is the Minimax Regret
Decision?
2. Data
collected on the yearly demand for 50-pound bags of fertilizer at Sunshine
Garden Supply are shown in the following table.
Year
Demand
for Fertilizer (1,000s of Bags)
1
4
2
7
3
5
4
5
5
10
6
7
7
8
8
9
9
11
10
14
11
15
1. Develop
a three-year moving average to forecast sales in year 12.
Year Demand for Fertilizer (1,000s of Bags)
1 0
2 0
3 0
4 5.333333333
5 5.666666667
6 6.666666667
7 7.333333333
8 8.333333333
9 8
10 9.333333333
11 11.33333333
12 13.33333333
2. Develop
a 3-year weighted average to predict demand in year 12, in which sales in the
most recent year is given a weight of 2
and sales in the two years prior to that are each given a weight of 1.
3. Develop
a regression/trend line to estimate the demand for fertilizer in year 12.
4. Based
on the three forecasts you have created, which forecast is the most accurate?
3. Kaplan
College has decided to “wire” its campus. The first stage in this
effort is to install the “backbone,” i.e., to connect all the
buildings. The table below gives the distances between the various buildings on
campus in hundreds of feet.
Distances in Hundreds of Feet
From
To
Building
1
Building
2
Building
3
Building
4
Building
5
Building
6
Building
1
3
7
5
5
4
Building
2
5
2
6
6
Building
3
5
4
4
Building
4
5
3
Building
5
4
Building
6
1. How
should the buildings be connected to minimize the total length of cable?
2. What
length of cable is required?
4. The following
represents the distances in miles from a warehouse (node 1) to various cities
in Montana. The major outlet store is located at node 7.
From
Node
To
Node
Distance
1
2
40
1
4
100
2
3
20
2
4
30
3
4
60
3
5
40
3
6
20
4
5
70
4
7
50
5
6
50
5
7
80
6
7
40
1. Find
the shortest route and distance from Node 1 to Node 7.
5. The network
of a city sewer system and their capacities are shown below. Remember that the
arc has both capacity and reverse capacity. For example, row 1 is the flow from
node 1 to node 2 and row 2 is the reverse flow from node 2 to node 1. There are
eight branches in this network.
From
Node
To
Node
Fluid
Flow
1
2
150
2
1
100
1
3
0
3
1
150
1
4
300
4
1
300
1
5
150
5
1
100
2
4
300
4
2
200
3
4
250
4
3
300
3
5
300
5
3
250
4
5
100
5
4
0
Determine
the maximum flow (in hundreds of gallons of water per minute) from node 1 to
node 5
6. The governor of Michigan believes
that the state can improve the states crime rate if the state can reduce the
college debt carried by its citizens and if they can increase the percent of
the population covered by health insurance.
1. Using the States Data Set and PHStat, create the multiple regression
prediction equation.
2. Predict the crime rate for
Michigan if the college debt were $25,000 and the percent not covered by
insurance was 10?
7. A
concessionaire for the local ballpark has developed a table of conditional
values for the various alternatives (stocking decisions) and states of nature
(size of crowd).
Stocking Decision
Large Crowd
($)
Average Crowd
($)
Small Crowd
($)
Large Inventory
$22,000
$12,000
-$2,000
Average Inventory
$15,000
$12,000
$6,000
Small Inventory
$9,000
$6,000
$5,000
If
the probabilities associated with the states of nature are 0.30 for a large
crowd, 0.50 for an average crowd, and 0.20 for a small crowd, determine:
1.
The
alternative that provides the greatest expected monetary value (EMV).
2.
The
expected value of perfect information (EVPI).
1. Even though
independent gasoline stations have been having a difficult time, Susan Solomon
has been thinking about starting her own independent gas station. Susans problem is to decide how large her
station should be. The annual returns
will depend on both the size of the station and a number of marketing factors
related to oil industry and demand for gasoline. After careful analysis, Susan developed the
following table:Sizes of Gasoline StationGood Market
($)Fair Market
($)Poor Market
($)Small $70,000$30,000-$30,000Medium$110,000$50,000-$40,000Large$170,000$70,000-$50,0001.
Develop a decision table for this
decision. 2.
What is the Maximax decision? 3.
What is the Maximin decision?
4.
What is the criterion of realism decision? 5. Develop
an Opportunity Loss Table6.
What is the Minimax Regret
Decision?2. Data
collected on the yearly demand for 50-pound bags of fertilizer at Sunshine
Garden Supply are shown in the following table. YearDemand
for Fertilizer (1,000s of Bags)14273545510677889911101411151. Develop
a three-year moving average to forecast sales in year 12. Year Demand for Fertilizer (1,000s of Bags)1 02 03 04 5.3333333335 5.6666666676 6.6666666677 7.3333333338 8.3333333339 810 9.33333333311 11.3333333312 13.333333332. Develop
a 3-year weighted average to predict demand in year 12, in which sales in the
most recent year is given a weight of 2
and sales in the two years prior to that are each given a weight of 1. 3. Develop
a regression/trend line to estimate the demand for fertilizer in year 12. 4. Based
on the three forecasts you have created, which forecast is the most accurate?3. Kaplan
College has decided to “wire” its campus. The first stage in this
effort is to install the “backbone,” i.e., to connect all the
buildings. The table below gives the distances between the various buildings on
campus in hundreds of feet.Distances in Hundreds of FeetFromToBuilding
1Building
2Building
3Building
4Building
5Building
6Building
137554Building
25266Building
3544Building
453Building
54Building
61. How
should the buildings be connected to minimize the total length of cable? 2. What
length of cable is required?4. The following
represents the distances in miles from a warehouse (node 1) to various cities
in Montana. The major outlet store is located at node 7. From
NodeTo
NodeDistance12401410023202430346035403620457047505650578067401. Find
the shortest route and distance from Node 1 to Node 7.5. The network
of a city sewer system and their capacities are shown below. Remember that the
arc has both capacity and reverse capacity. For example, row 1 is the flow from
node 1 to node 2 and row 2 is the reverse flow from node 2 to node 1. There are
eight branches in this network.From
NodeTo
NodeFluid
Flow1215021100130311501430041300151505110024300422003425043300353005325045100540Determine
the maximum flow (in hundreds of gallons of water per minute) from node 1 to
node 56. The governor of Michigan believes
that the state can improve the states crime rate if the state can reduce the
college debt carried by its citizens and if they can increase the percent of
the population covered by health insurance. 1. Using the States Data Set and PHStat, create the multiple regression
prediction equation. 2. Predict the crime rate for
Michigan if the college debt were $25,000 and the percent not covered by
insurance was 10?7. A
concessionaire for the local ballpark has developed a table of conditional
values for the various alternatives (stocking decisions) and states of nature
(size of crowd).Stocking DecisionLarge Crowd
($)Average Crowd
($)Small Crowd
($)Large Inventory$22,000$12,000-$2,000Average Inventory$15,000$12,000$6,000Small Inventory$9,000$6,000$5,000If
the probabilities associated with the states of nature are 0.30 for a large
crowd, 0.50 for an average crowd, and 0.20 for a small crowd, determine:1.
The
alternative that provides the greatest expected monetary value (EMV).2.
The
expected value of perfect information (EVPI).
