MGMT 455 Midterm Exam Part1
Cal State East Bay
By completing and submitting the answer to the exam, the student fully understands the university’s policy on academic dishonesty and agree to abide by this policy.
Policy on Academic Dishonesty:
By enrolling in this class the student agrees to uphold the standards of academic integrity described in the catalog at http://www.csueastbay.edu/ecat/current/i-120grading.html#section12.
Cheating will result in: 1) a zero score and the loss of all grading options; and/or 2) an “F” grade; and/or 3) referral to the Academic Vice President for expulsion from the University.
1. Please answer all of the questions in the attached excel file. Submit the excel file only.
2. Submit the excel file with all your answer in the BlackBoard.
3. Name the excel file as LastName_FirstInition_Exam1. (E.g., Wang_L_Exam1)
4. If you are unable to run the Solver, take a screenshot of the solver parameters window and paste it on the corresponding spreadsheet. (In this case, I can still give you partial credit even if your answer was wrong.)
Part I: Linear Programing (60 pts in total)
1. Linear Programing problem – formulation and solving process (30 pts)
A furniture manufacturer produces two types of tables (country and contemporary) using two types of machines. The time required to produces the tables on each machine is given in the following table.
Machine Country Contemporary Total Machine Time Available per Week
Router 1.5 2.0 1,000
Sander 3.0 5.0 2,000
Country tables sell for $350 and contemporary tables sell for $500. Management has determined that at most 20% of the total amount of two types of tables made should be country.
a) Formulate an LP model. Notice: please show clearly the definition of decision variables, objective function, and each one of the constraints. Please write the complete formulation in the worksheet “Que 1” in the excel file. (10 pts)
b) Create a spreadsheet model for this problem and solve it using Solver. Please show your work in the same worksheet “Que 1” in the excel file. (If you encounter system error or you can’t find the solution, please take a screenshot when you set up the Solver window, then paste it in the same worksheet.) (15 pts)
c) What is the optimal amount for each type of tables and the optimal total profit? (Highlight the answers in the worksheet or answer that in your own words. ). (5 pts)
2. Linear Programing problem – formulation and solving process (30 pts)
A hospital emergency room is open 24 hours a day. Nurses report for duty at 1am, 5am , 9am, 1pm, 5pm, or 9pm, and each works an 8-hour shift. Nurses are paid the same, regardless of the shift they work. The following table shows the minimum number of nurses needed during the six-periods into which the day is divided. How should the hospital schedule the nurses so that the total staff required for one day’s operation in minimized?
SHIFT TIME NURSES NEEDED
1 1-5 am 4
2 5-9 am 13
3 9 am-1 pm 17
4 1-5 pm 10
5 5-9 pm 12
6 9 pm -1 am 5
a) Please formulate this problem. Show clearly the decision variables, objective function and constraints functions. Please write the complete formulation in the worksheet “Que 2” in the excel file. (5 pts) (Hint: you may define x1 as the number of the nurses starts at the Shift 1.)
b) Create a spreadsheet model for this problem and solve it using Solver. Please show your work in the same worksheet “Que 2” in the excel file. If you encounter any problems, please take a screenshot when you set up the Solver window, then paste it in the same worksheet. (15 pts)
c) What is the optimal amount for the nurses at each Shift? And what is the optimal total number of nurses? (Highlight the answers in the worksheet or answer that in your own words). (10 pts)
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