Student ID #:
This exam consists of 28 (T/F and multiple-choice) questions.
Please answer on the scantron sheet provided. I will not be responsible for lost sheets that are turned in unstapled.
Please note that you have to enter your name and Student ID number in the above area. Failure to do so will result in a grade of zero on the part of the exam in which the relevant details have not been entered.
On the exam the following acronyms may have been used:
LP – Linear Program/Programming
IP – Integer Program/Programming
ILP – Integer Linear Program/Programming (used synonymously with IP)
NLP – Non-linear Program/ Programming
MILP – Mixed Integer Linear Program/ Programming
An “(s)” appended to these acronyms denotes the plural.
This is an open book exam. Be sure to allocate your time wisely. All the best.
Answer the next six questions based on the case given below:
Tower Engineering Corporation is considering undertaking several proposed projects for the next fiscal year. The projects, the number of engineers and the number of support personnel required for each project, and the cost for each project are summarized in the following table:
Formulate an integer linear program that maximizes Tower’s profit, subject to constraints, which will be stated in the questions that follow.
Let Pi = 0 or 1, indicate if project i will not be undertaken or will be undertaken respectively.
For the next two questions, consider the network below.
Consider the LP for finding the shortest-route path from node 1 to node 7. Bidirectional arrows («) indicate that travel is possible both ways. Let Xij = 1 if the route from node i to node j is taken and 0 otherwise.
Read the following case and answer the four questions that follow:
A professor has been contacted by not-for-profit agencies that are willing to work with student consulting teams. The agencies need help with such things as budgeting, information systems, coordinating volunteers, and forecasting. Although each of the five student teams could work with any of the agencies, the professor feels that there is a difference in the amount of time it would take each group to solve each problem. The professor’s estimate of the time, in days, is given in the table below.
Let Xij denote if team i (A=1,B=2,C=3,D=4, E=5) is assigned to project j (Budgeting =1, Information = 2, Volunteers =3, Forecasting = 4)
For the next six questions, consider the following: Burnside Marketing Research conducted a study for Barker Foods on some designs for a new dry cereal. Three attributes were found to be most influential in determining which cereal had the best taste: ratio of wheat to corn in the cereal flake, type of sweetener (sugar, honey, or artificial), and the presence or absence of flavor bits. Nine children participated in taste tests and provided the following part-worths for the attributes:
|Wheat/ Corn||Sweetener||Flavor Bits|
Child Low High Sugar Honey Artificial Present Absent
1 35 25 40 30 35 20 26
2 38 40 35 42 30 26 21
3 45 40 40 42 35 26 21
4 25 30 50 45 45 16 28
5 35 20 50 45 30 18 14
6 15 25 50 55 45 19 16
7 39 41 25 40 30 30 31
8 30 35 35 40 45 28 26
9 30 18 50 55 40 26 16
Assume that the overall utility (sum of part-worths) of the current favorite cereal is 100 for each child. Your job is to design a product that will maximize the share of choices for the nine children in the sample.
Answer the next three questions based on the case given below:
Hansen Controls has been awarded a contract for a large number of control panels. To meet this demand, it will use its existing plants in San Diego and Houston, and consider new plants in Tulsa, St. Louis, and Portland. Finished control panels are to be shipped to Seattle, Denver, and Kansas City. Pertinent information is given in the table.
|Shipping Cost to Destination:||
|1- San Diego||—-||5||7||8||12,000|
|4- St. Louis||500,000||12||4||2||7,000|
We develop a transportation model as an LP that includes provisions for the fixed costs (construction costs in this case) for the three new plants. The solution of this model would reveal which plants to build and the optimal shipping schedule.
|Let||xij = the number of panels shipped from source i to destination j|
|yi = 1 if plant i is built, = 0 otherwise (i = 3, 4, 5)|
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