ESI6314_midterm_FALL09

# ESI6314_midterm_FALL09 - ESI 6314 y1 y2 1 2 Midterm Exam 2...

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y1 y2 1 2 2 1 -1 isoprofit line Midterm Exam ESI 6314 Deterministic Methods in Operations Research ver. 1 October 21, 2009 Instructor: Dr. Vladimir L. Boginski Research and Engineering Education Facility University of Florida Duration: 75 minutes Rules: Closed books, closed notes. Calculators are allowed. It is important that you show details of your work, where appropriate. Please return questions along with your answers. The UF Honor Code: "We, the members of the University of Florida community, pledge to hold ourselves and our peers to the highest standards of honesty and integrity." "On my honor, I have neither given nor received unauthorized aid in doing this assignment." NAME:

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1.(20 points) A post office requires different number of full-time employees on different days of the week. The number of full-time employees required on each day is given in the table below. Union rules state that each full-time employer must work five consecutive days and then receive two days off. For example, an employee who works Monday to Friday must be off on Saturday and Sunday. But the post office can force employees to work one day of overtime each week. For example, an employee whose regular shift is Monday to Friday can also be required to work on Saturday. Each employee is paid \$50 a day for each of the first five days worked during a week and \$62 for the overtime day (if any). The post office wants to meet its daily requirements using only full-time employees. Formulate an LP whose solution will enable the post office to minimize the cost of meeting its weekly work requirements. Day Number of Full-time Employees Required 1 = Monday 17 2 = Tuesday 13 3 = Wednesday 15 4 = Thursday 19 5 = Friday 14 6 = Saturday 16 7 = Sunday 11 Let x 1 = Number of employees who start work on Sunday and work 5 days, x 2 = Number of employees who start work on Monday and work 5 days. .. x 7 = Number of employees who start work on Saturday and work 5 days. Also let o1 = Number of employees who start work on Sunday and work 6 days. .. o7 = Number of employees who start work on Saturday and work 6 days. Then the appropriate LP is min z = 250(x 1 +x 2 +...x 7 ) + 312(o1+o2+. ..o7) s.t. x 1
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ESI6314_midterm_FALL09 - ESI 6314 y1 y2 1 2 Midterm Exam 2...

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