WHITE
______
NAME
ISDS 361B
SAMPLE EXAM #2
Open Book, Notes, etc.
1. (20) ______
2. (30) ______
3. (25) ______
4. (30) ______
TOTAL (105) ______
A score of 100 will be considered perfect!
1. Frank Hurley is a farmer in Ames, Iowa.
· He has 300 acres on which he wishes to plant wheat and corn for the season.
· For crop rotation purposes he must plant at least 100 acres of each crop.
· He can participate in a federal program that will require him to produce at least as much wheat as corn. Under this program, he is guaranteed to earn $150 per acre of wheat planted and $200 per acre of corn planted.
· Alternatively he can opt not to participate in the program in which case he projects he would make only $120 per acre of wheat planted and $195 per acre of corn planted, but there would be no requirement to produce at least as much wheat as corn.
· His goal is to maximize his total profit for the season.
a. If Frank did participate in the program
How many acres of wheat should he plant?
How many acres of corn should he plant?
What is his total expected profit?
b. If Frank did not participate in the program
How many acres of wheat should he plant?
How many acres of corn should he plant?
What is his total expected profit?
What would you recommend to Frank?
2. Coolbike Industries is a small start-up company run by Linh Phan and family in Garden Grove, California, that manufactures boys and girls bicycles in both 20-inch and 26-inch models that it then sells over the internet. Thus far, demand for the bicycles has been great enough that the company has been able to sell all the bicycles that it manufactures.
The table below gives the gross unit profit that includes the material and labor for each bicycle as well as the number of minutes required for the production of each bicycle frame and the assembly time required to install the chain pedals and wheels for each model.
Bicycle / Unit Profit / Production Minutes / Assembly Minutes20-inch girls / $27 / 12 / 6
20-inch boys / $32 / 12 / 9
26-inch girls / $38 / 9 / 12
26-inch boys / $51 / 9 / 18
· Each week Coolbike produces at least 200 girls models and 200 boys models.
· Production of the bicycles occurs in a small plant just off Garden Grove Blvd. The plant runs two (8-hour) shifts per day, 5 days (Monday - Friday) per week.
· At the end of each day, the completed frames are packed up and sent to another small assembly area (actually a garage owned by Linh Phan) off Westminster Ave. where the frames and the other bicycle parts are assembled to give the finished product. This area also operates two 8-hour shifts, 5 days a week (Tuesday - Saturday).
· This week there are 500 tires available for 20-inch models and 800 tires available for 26-inch models.
(a) Determine Coolbike’s optimal production schedule for the week..
20-inch girls ______20-inch boys ______26-inch girls ______26-inch boys ______
What gross profit will it realize for the week? ______
(b) 20-inch tires currently cost Coolbike $8.50 each and 26-inch tires $9.75 each.
· Discuss how much Coolbike should be willing to pay for additional tires above the 500 20-inch tires and the 800 26-inch tires that are currently available.
· Discuss for how many extra tires of each size your statement above is valid.
(c) Would the solution in (a) still be the optimal solution if the company underestimated the profit on:
· Girls 20-inch bikes by $1 ______Why or why not? ______
· Boys 20-inch bikes by $1 ______Why or why not? ______
· Girls 26-inch bikes by $1 ______Why or why not? ______
· Boys 26-inch bikes by $1 ______Why or why not? ______
(d) How much would the gross profit improve if you relaxed the minimum number of
· Girls bikes produced to 175? ______Why? ______
· Boys bikes produced to 175? ______Why? ______
(e) Suppose that the number of 20-inch bikes produced should not exceed more than 40% of the total production. Using a definitional variable write the appropriate constraints that would modify your model. You do not have to re-solve the model.
3. MVC Enterprises can manufacture 4 different computer models:
Processor / Celeron / Pentium III / Celeron / Pentium III
Hard Drive / 10 gb / 10 gb / 10 gb / 15 gb
Floppy Drives (1.44mb) / 1 / 1 / 2 / 1
Zip Drive / YES / YES / NO / YES
Audio/Video / CD / DVD / DVD / DVD
Monitor / 15” / 15” / 17” / 17”
Cases / Min-Tower / Tower / Tower / Mini-Tower
Production Time (hrs.) / .4 / .5 / .6 / .8
Unit Profit / $130 / $150 / $200 / $250
· MVC must satisfy a contract that produces a minimum of 200 MVC-Net’s per week.
· The following resources are available weekly:
Processors Hard Drives Other Drives
Celeron 700 10 gb 800 Floppy 1400
Pentium III 550 15 gb 950 Zip 1000
Audio Visual Monitors Cases
CD 600 15” 850 Mini-Tower 1250
DVD 900 17” 750 Tower 300
· MVC employs 20 workers each of whom average 30 production hours each per week.
(a) Formulate this problem as a linear program and solve for the optimal weekly production schedule for MVC. Fill in the recommended production quantities in the table below.
MVC-Student / MVC-Plus / MVC-Net / MVC-Pro / Total Weekly Profit(b) What is the minimum profit for the MVC-Plus that would justify their production?
Explain.
(c) If you could purchase additional Celeron processors for $4 more than what you are currently paying for them, would you do this?
Explain.
(d) Suppose you could add an additional worker for $1000 per week. Remember workers average 30 hours per week. Should you do this?
Explain.
4. Universal Travel is planning to move its headquarters from Cincinnati to Columbus, Ohio. The following are the steps that must be taken. Times are in weeks.
Optimistic Most Likely Pessimistic
Time Time Time
A-- Select a site 8 12 20
B-- Refurbish Building 9 10 12
C-- Determine Which Staff Will 2 2 3
Transfer
D-- Hire Local Staff Replacements 3 6 8
In Columbus
E-- Pack Boxes in Cincinnati 1 2 5
F-- Move Equipment 2 3 4
G -- Move Files 1 2 5
H -- Set Up Equipment/Files 3 4 5
In Columbus
I -- Occupancy 5 6 14
· The project begins by selecting a site and determining which staff will transfer
· Once the site has been selected the building on the site can be refurbished
· Once it is determined which staff will transfer, local replacements in Columbus can be hired
· When a site has been selected and it is has been determined which staff will transfer, boxes can be packed in Cincinnati
· Equipment will be moved once the building has been refurbished
· Files will be moved when the building has been refurbished and the boxes (which include the files) have been packed
· When both the equipment and the files have been moved, their setup in Columbus can take place
· The building will be occupied once the two Columbus operations (hiring local replacements and setting up equipment and files) have been completed
a. Draw a PERT/CPM network below that models this situation. Check it carefully!
b. To solve this problem, what distribution are you assuming for the completion times for each of the activities?
What 3 assumptions do you have to make to be able to use the PERT approach for this model?
c. Now assume the assumptions in part b are satisfied.
What is the expected completion time of the project?
What is the critical path?
d. What is the probability the project is completed within 36 weeks?
Now suppose Universal will be charged for both sites if it is not completely moved in within 36 weeks. This will cost the company $6000.
e. For $1200, additional movers can be hired to move the files, cutting each of the three time estimates for that activity in half. Additionally, for $1200, additional movers can be hired to assist in moving the equipment, cutting the three time estimates for that activity by 1 week each. The company can pursue 4 options:
(1) Do not hire any additional personnel
(2) Hire the movers to move files only
(3) Hire the movers to move equipment only
(4) Hire movers to move both files and equipment
What is your recommendation?
Why?