CIS 468 Midterm Exam
Instructions:
Please be sure to:
· Make sure you have the exam paper with your name on it.
· Clearly indicate your answers to each question
· At the end of the exam, upload your Excel file(s) for questions 1 & 3
o You may upload multiple files.
o Your Excel work will not be graded, but it will allow me to see how you arrived at your answer. You must upload a file in order to receive full credit for questions 1 & 3 only.
During the exam:
· During the exam you MAY use any notes, books, internet/Google, gen AI or Blackboard materials.
· You MAY NOT communicate with or give or receive help to anyone else (a student in the class or someone external). Any evidence of collaboration will result in an academic integrity report being filed.
· To be fair to everyone, I do not answer questions or help with Python/R/Excel/Solver/technical issues during the exam.
o Do your best to interpret and answer the question.
o If you want to leave me a comment, you can write a note in the optional free response page at the end of the exam.
1. The coach of a swim team needs to assign swimmers to a 200-yard medley relay team. A relay team consists of four swimmers, each of whom swims 50 yards of one of the four strokes. Since most of the best swimmers are very fast in more than one stroke, it is not clear which swimmer should be assigned to each of the four strokes. The five fastest swimmers and the best times (in seconds) they have achieved in each of the strokes (for 50 yards) are shown in Table 1, as well as in MidtermReview_1_RelayTimes.csv posted on Blackboard.
Table 1: Times (seconds) by Swimmer and Stroke
Formulate a LP model that can be used to select which swimmer should swim each of the four strokes in order to create a relay time with the fastest total time.
a. What is the total time in the optimal solution?
b. Which stroke will each swimmer swim in the optimal solution?
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Backstroke |
Breaststroke |
Butterfly |
Freestyle |
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2. The Electro-Poly Corporation is the world's leading manufacturer of slip rings. A slip ring is an electrical coupling device that allows current to pass through a spinning or rotating connection such as a gun turret on a ship, aircraft or tank. The company recently received a $750,000 order for various quantities of three types of slip rings. Each slip ring requires a certain amount of time to wire and harness. Table 1 summarizes the requirements for the three models of slip rings.
Table 1: Requirements
Electro-Poly does not have enough wiring and harnessing capacity to fill the order by its due date. The company only has 10,000 hours of wiring capacity and 5,000 hours of harnessing capacity available to devote to this order. However, the company can subcontract any portion of this order to one of its competitors. The unit costs of producing each model in-house and buying the finished products from a competitor are summarized in Table 2.
Table 2: Costs
Management would like to optimize their production in order to fill the customer order at the least cost possible.
An analyst used Excel Solver to formulate a LP problem to calculate how many slip rings Electro-Poly should make and how many they should buy. The model and the output are shown on the next two pages.
a. Interpret the shadow price (pi) of the Wiring Capacity constraint.
b. Suppose workers in the Harnessing area can work overtime shifts at an additional cost of $6.00 per hour. Should Electro-Poly schedule these workers to work overtime to complete these orders?
3. An environmental firm is planning a collection project in order to add to their inventory of algae samples. They can order any number of algae bloom samples from any of seven lakes in the region. The cost per sample from each lake is shown in Table 1 below. Each lake also has its own balance of algae populations, described in Table 2 below. For example, a sample from Lake Barkley has a 14% probability of being identified in the lab as Type C and 13% probability of Type F, etc. The firm wants to be sure that in the end they have at least 1000 algal units for each algae type. They also want to make sure that no more than 20% of the samples come from any one lake. How many samples should the firm order from each lake in order to minimize their total cost and meet their requirements?
Table 1: Cost of Sample for each Lake
Table 1: Algae Population Composition by Lake
Formulate a LP model to analyze how many samples the firm should order from each lake in order to minimize their total cost and meet their requirements. An Excel file with the problem data is posted on Blackboard to help get you started.
a. What are the decision variables for this problem?
b. Write an expression for the constraint that 1,000 algal units of Type_D algae are required.
c. What is the minimum cost achievable in this scenario?
d. If the firm could select one algae type and lower its requirement to 900 algal units, which algae type should it select? Explain how you arrived at your answer.
This is an optional additional space for you to write any comments that you had about the exam. (This question will not be graded.)