Ag Bus 328
Final
Section 1
12/12/14
Dr. Hurley
General Instructions: This exam is worth 200 points. You must provide your own paper. You
are allowed to use your notes for the exam. You must show all your work when appropriate to
get credit. Create a new tab for each question you answer. No cell phones are allowed to be in
your possession during the exam. If you are caught with a cell phone, you will receive a zero on
the exam. (Please note that except for any diagrams or mathematical models, all answers
should be entered into a textbox on your spreadsheet and the answers should be kept brief and
to the point.)
GOOD LUCK!
Question A: Given the model below, answer the following questions.
max
𝑤.𝑟.𝑡.𝑥1 ,𝑥2
6𝑥1 + 4𝑥2
Subject to:
2𝑥1 + 2𝑥2 ≤ 24
6𝑥1 + 2𝑥2 ≤ 60
2𝑥1 + 4𝑥2 ≤ 40
𝑥1 ≥ 0, 𝑥2 ≥ 0
Question 1: What is the dual to this problem (5 Points)?
Question 2: Solve the dual problem using the tabular form of the simplex method (20 Points).
Make sure to interpret the table, i.e., what are the values for each decision variable.
Question 3: Develop a spreadsheet model for the dual problem and solve it using Solver making
sure to run a sensitivity report (10 Points).
Question 4: Calculate the allowable ranges for each of the coefficients in the objective function
and the right hand side of the constraint (5 Points). There is no need to explain what they mean.
Question 5: If all of the objective coefficients decreased by 7% could you definitely say
whether the optimal answer would change without resolving the problem? Please explain (10
Points).
Page 1 of 5
Revised: 12/3/14
Question B: Suppose you are a large apple producer who has operations in New York,
Pennsylvania, South Carolina, and Florida. In this coming week, you have the equivalent of 200
truckloads of apples that you need to get from your east coast operations to retailers on the west
coast. Based on the time of year, you have 44 truckloads worth of apples in Florida, 36
truckloads in South Carolina, 30 truckloads originating from Pennsylvania, and another 90
truckloads available at your New York operation.
There are two locations on the west coast that you need to deliver your apples: Oregon and
Idaho. To meet the needs of your Oregon retailers, you will need to get 120 truckloads to them,
while you will need 80 truckloads of apples for retailers in Idaho.
In order to get your apples from the east coast to the west coast, you will need to make a couple
of stops in between due to a new set of national trucking regulations. These regulations have
established that only regionally licensed truckers can haul product from certain states to certain
states. At each intermediary stop, the current truck driver will unhitch the trailer full of apples so
that the other driver who is allowed into the next region can hitch it to his own truck. In this case
Pennsylvania and New York truckers can make deliveries to Illinois. Truckers from Florida and
South Carolina are able to deliver products to Tennessee. Truckers from Tennessee have the
ability to deliver apples to Oklahoma and Iowa. Truckers in Illinois can also drive trucks to
Iowa, as well as, South Dakota. Truckers from Oklahoma and Iowa are able to deliver products
to Oregon. Iowa truckers also have the ability to deliver apples to Idaho. Furthermore, South
Dakota truckers can also make deliveries to Idaho.
Each regional trucking company is constrained by the number of drivers each has available to
haul product. To haul a truckload of apples from one region to the next, you need one driver per
truckload. In Pennsylvania, 34 truckers are available to ship apples to Illinois, while New York
has 104 drivers that can be allocated to ship apples to Illinois. In Florida, there are 60 truckers
available to go to Tennessee while South Carolina has 42 truckers who can take apples to
Tennessee. Illinois has 24 truckers who can take apples to South Dakota and 98 truckers who
can go to Iowa for this task. In Tennessee, there are 90 truckers available to ship product to
Oklahoma and 32 truckers who can be used to ship apples to Iowa. Oklahoma has 96 truckers
that can drive to Oregon, while Iowa has 46 truckers who can drive to Oregon. Iowa has 70
truckers available to ship apples to Idaho, while South Dakota has 30 truckers who can move
apples to Idaho.
To ship apples from New York to Illinois, it will cost your company $1,150 per truckload. At
$1,450 per truckload, you can ship apples from South Carolina to Tennessee and from
Pennsylvania to Illinois. The most expensive shipping cost for apples is $1,600 per truckload
from Illinois to South Dakota. It costs you $1,400 per truckload to send apples from Iowa to
Idaho and Florida to Tennessee. At $1,500 per truckload, you are able to ship apples from
Tennessee to Oklahoma. Your cheapest shipping cost at $1,000 per truckload is from Tennessee
to Iowa. It costs you $1,350 to ship a truckload of apples from Illinois to Iowa. A truckload of
apples from Iowa to Oregon and from South Dakota to Idaho will cost you $1,050 per truckload.
Finally, to ship a truckload of apples from Oklahoma to Oregon, it will cost you $1,100 per
truckload.
Page 2 of 5
Revised: 12/3/14
Since you negotiated at the beginning of the year with the retailers on the west coast a fixed price
for the apples, your goal is to minimize the shipment cost to get the apples to your customers.
Answer the following questions based on the above.
1. Please develop a visual diagram that represents this problem. (10 Points)
2. Please build a mathematical model that represents this problem. (20 Points)
3. Please build a spreadsheet model that represents this problem. (15 Points)
4. Solve this problem using Solver.
a. What is the optimal amount of apples shipped from the supplying states to the
demanding states and what is the minimum cost to meet these requirements? (5
Points)
5. Suppose that cost was not an issue and you had no constraints on the supply or demand of
apples. Please build a spreadsheet model that represents this new problem which
maximizes the amount apples you can take from the east coast to the west coast. (15
Points)
6. Solve this new problem using Solver.
a. What is the optimal amount of apples shipped from the supplying states to the
demanding states and what is the maximum amount of apples you can get through
the transportation system? (5 Points)
7. Given the information in part 5 above, suppose that only Tennessee or Illinois can ship to
Iowa but not both. Please write a set of mathematical constraints that will allow for the
maximization of flow given this new constraint. (15 Points)
8. Please build a spreadsheet model that represents this new problem and solve it for the
maximum flow given this new constraint. (10 Points)
Page 3 of 5
Revised: 12/3/14
Question C: Suppose you are a consultant to a local retailer who is opening a new store in the
area. You have been hired to coordinate all the tasks required to open the store in the next 35
weeks. Below you will find all the activities that will need to be done to get the new store
operational.
Activity
A
B
C
D
E
F
G
H
I
J
K
L
M
Description Immediate
Predecessor
Find Location
N/A
Find
A
Distributors
Develop
A
Promotional
Plan
Hire
A
Contractors
Design Floor
A
Layout
Hire Managers
B,C
Retrofit Outside D,E
Train Managers F
Stock Shelves
F,G
Hire Regular
G
Employees
Contact News
H,I
Outlets
Clean Store
I,J
Do Final
K,L
Opening
Preparation
Check
Time Required
in Weeks
Normal Crash
Cost in 100 of
Dollars
Normal Crash
4
8
1
4
$160
$60
$220
$100
5
2
$66
$132
3
2
$10
$24
6
5
$160
$240
4
7
12
2
3
2
3
7
1
1
$90
$60
$100
$4
$50
$190
$220
$130
$8
$150
9
5
$40
$160
4
2
2
1
$2
$16
$4
$32
Page 4 of 5
Revised: 12/3/14
Answer the following questions based on the above set-up.
1. Construct a project network for this project. (10 Points)
2. What are all the paths and path lengths for this project? Which path is the critical path?
Could you finish this project in the allotted 35 weeks (10 Points)?
3. What are the earliest start and finish times, the latest start and finish times, and the slack
time for each activity? Does this confirm that the critical path you found earlier is the
true critical path? (15 Points)
4. How much is this project going to cost assuming you crash no activities? (5 Points)
5. If you had to do this project in 35 weeks, what is the lowest cost you could do the project
for? What activities would be crashed? (Please note that except for any diagrams or
mathematical models, all answers should be entered into a textbox on your spreadsheet
and the answers should be kept brief and to the point.) (15 Points)
Page 5 of 5
Revised: 12/3/14