# During normal weekday operations the number of

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During normal weekday operations, the number of officers needed varies on the time of day. The staff guidelines require the following minimum number of officers on duty: Minimum Number Needed Shift 1: 8 am to noon 5 Shift 2: Noon to 4 pm 6 Shift 3: 4 pm to 8 pm 10 Shift 4: 8 pm to midnight 7 Shift 5: midnight to 4 am 4 Shift 6: 4 am to 8 am 6 What is the LP model to determine the minimum number of officers required to report for each shift? Use x i for the decision variables. 12. Use the following Management Scientist output to answer the questions. a. Give the solution to the problem. b. Which constraints are binding? c. What would happen if the coefficient of x 1 increased by 3? d. What would happen if the right-hand side of constraint 1 increased by 10? LINEAR PROGRAMMING PROBLEM MAX 31X1+35X2+32X3 S.T. 1) 3X1+5X2+2X3>90 2) 6X1+7X2+8X3<150 3) 5X1+3X2+3X3<120 Comm 251 F04 Page 3 of 6 Term Exam 1

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OPTIMAL SOLUTION Objective Function Value = 763.333 Variable Value Reduced Costs ---------- ------- ------------------ X1 13.333 0.000 X2 10.000 0.000 X3 0.000 10.889 Constraint Slack/Surplus Dual Prices -------------- ---------------- ------------------ 1 0.000 -0.778 2 0.000 5.556 3 23.333 0.000 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit ------------ ------------------- ---------------- --------------- X1 30.000 31.000 No Upper Limit X2 No Lower Limit 35.000 36.167 X3 No Lower Limit 32.000 42.889 RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit ------------- --------------- ---------------- --------------- 1 77.647 90.000 107.143 2 126.000 150.000 163.125 3 96.667 120.000 No Upper Limit Comm 251 F04 Page 4 of 6 Term Exam 1
Use this graph to answer the questions. 0 5 10 15 0 5 10 15 I II III IV V A B C D E Max 20X + 10Y s.t. 12X + 15Y < 180 15X + 10Y < 150 3X -8Y < 0 X , Y > 0 a. Which area (I, II, III, IV, or V) forms the feasible region? b.

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During normal weekday operations the number of officers...

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