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F04MT1ver1withanswers

Right hand side ranges constraint lower limit current

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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
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13. 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. Which point (A, B, C, D, or E) is optimal? c. Which constraints are binding? d. Which slack variables are zero? Comm 251 F04 Page 5 of 6 Term Exam 1
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UNIVERSITY OF NORTHERN BRITISH COLUMBIA – SCHOOL OF BUSINESS Comm 251: Introduction to Management Science – F04 Term Exam 1 Name: ____________________________ Student Number: __________________ Please use pen and place “0” around choice. Do not use whiteout. 1. a b c d 2. a b c d 3. a b c d 4. a b c d 5. a b c d 6. a b c d 7. a b c d 8. a b c d 9. a b c d 10. a b c d Comm 251 F04 Page 6 of 6 Term Exam 1
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Exam 1 Answers 1. ANSWER: a 2 .ANSWER:a 3 ANSWER: b 4 .ANSWER:a 5 .ANSWER:b 6 ANSWER: d 7. ANSWER: b 8. ANSWER: c 9 ANSWER: b 10. ANSWER: b 11. Let x 1 = the number of officers scheduled to begin at 8:00 a.m. x 2 = the number of officers scheduled to begin at noon x 3 = the number of officers scheduled to begin at 4:00 p.m. x 4 = the number of officers scheduled to begin at 8:00 p.m. x 5 = the number of officers scheduled to begin at midnight x 6 = the number of officers scheduled to begin at 4:00 a.m. The objective function to minimize the number of officers/nurses required is as follows: Min x 1 + x 2 + x 3 + x 4 + x 5 + x 6 The constraints require the total number of officers of duty each of the six four-hour periods to be at least equal to the minimum officer requirements. The constraints for the six four-hour periods are as follows: Time of Day 8:00 a.m. - noon x 1 + x 6 5 noon to 4:00 p.m. x 1 + x 2 6 4:00 p.m. - 8:00 p.m. x 2 + x 3 10 8:00 p.m. - midnight x 3 + x 4 7 midnight - 4:00 a.m. x 4 + x 5 4 4:00 a.m. - 8:00 a.m. x 5 + x 6 6 x 1 , x 2 , x 3 , x 4 , x 5 , x 6 0 Comm 251 F04 Page 7 of 6 Term Exam 1
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12. a. x 1 = 13.33, x 2 = 10, x 3 = 0, s 1 = 0, s 2 = 0, s 3 = 23.33, z = 763.33 b. Constraints 1 and 2 are binding. c. The value of the objective function would increase by 40. d. The value of the objective function would decrease by 7.78. 13. a. Area III is the feasible region b. Point D is optimal c. Constraints 2 and 3 are binding d. S 2 and S 3 are equal to 0 Comm 251 F04 Page 8 of 6 Term Exam 1
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