Question 1. (30 Points)
A project designed to refurbish a hospital operating theatre consists of activities A,B,C,D,E F, G and ,H, The estimated times (optimistic, most-likely and pessimistic times) and precedence relationships shown are as shown.
| Activity | Immediate Predecessors | Optimistic Time (O) | Most Likely Time (M) | Pessimistic Time (P) |
| A | - | 5 | 6 | 7 |
| B | A | 10 | 13 | 28 |
| C | A | 1 | 2 | 15 |
| D | A | 8 | 9 | 16 |
| E | B | 25 | 36 | 41 |
| F | B,C,D | 6 | 9 | 18 |
| G | D | 7 | 12 | 17 |
| H | E,F,G | 12 | 15 | 24 |
- Construct a network diagram for the refurbishment project (6 Points)
- Determine the project critical path and hence the project duration, d (7 Points)
- Find the standard deviation of the expected project duration (project duration) (4 Points)
- Determine the float of the project activities and interpret
- Using the expected duration obtained in (b) and the standard deviation in (c) above, find the probability that the project will be completed in
- Between 65 and 75 days (4 Points)
- Between 55 and 70 days (6 Points)
- Beyond 71 days (3 Points)
A project designed to refurbish a hospital operating theatre consists of activities A,B,C,D,E F, G and ,H, The estimated times (optimistic, most-likely and pessimistic times) and precedence relationships shown are as shown. Activity Immediate Optimistic Most Likely Pessimistic Predecessor Time (0) Time (M) Time (P) S A 5 6 7 . A 10 13 28 A 1 2 15 1 D A 8 9 16 E B 25 36 41 F. B,C,D 6 9 18 G D 7 12 17 H E,F,G 12 15 24 Standard Normal Probabilities Table entry Table entry for z is the area under the standard normal curve to the left of z. Z .00 .01 .02 .03 .05 .06 .07 .08 .09 .0003 .0005 .0007 .0009 .0013 .0018 .0025 .0034 .0045 .0060 .0080 .0104 .0136 .0174 ,0222 0222 .0281 0201 .0351 ,0003 .0004 .0006 .0009 .0012 .0017 .0023 .0032 .0043 .0057 , .0003 .0004 .0005 .0008 .0011 .0015 .0021 .0028 .0038 .0051 .0068 .0089 .0116 .0150 .0192 .0054 .0075 .0244 -3.4 -3.3 -3.2 -3.1 -3.0 -2.9 -2.8 -2.7 -2.6 -2.5 -2.4 -2.3 -2.2 -2.1 -2.0 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 42 -1.3 -1.2 -1.1 -1.0 0.9 -0.8 -0.7 2 -0.6 -0.5 -0.4 -0.3 -0.2 0.1 -0.0 .0003 .0005 .0007 .0010 .0013 .0019 .0026 .0035 .0047 .0062 .0082 .0107 .0139 .0179 .0228 0228 .0287 .0359 .0446 .0548 .0668 .0808 POCO .0968 we .1151 .1357 20 .1587 .1841 2119 .2420 2743 .3085 .3446 .3821 .4207 4602 .5000 .0003 .0005 .0006 .0009 .0013 .0018 .0024 0033 .0044 .0059 .0078 .0102 .0132 0170 .0217 .0274 .0344 0427 0526 .0643 0779 .0778 02 .0934 4444 .1112 2014 .1314 .1539 1200 .1788 2061 .2358 2676 .3015 .3372 .3745 4129 4522 4920 .0436 .04 .0003 .0004 .0006 .0008 .0012 .0016 .0023 .0031 .0041 .0055 .0073 .0096 .0125 .0162 .0207 .0262 .0329 0409 .0505 0618 .0749 .0901 076 .1075 1024 .1271 4400 .1492 1534 .1736 .2005 .2296 2611 .2946 .3300 .3669 .4052 .4443 .4840 .0003 .0003 .0004 .0004 0006 0006 ,0008 .0008 .0011 .0011 .0016 .0015 .0022 .0021 .0030 .0029 0040 .0039 .0052 .0071 .0069 .0094 .0091 0122 .0119 .0158 .0154 .0202 .0197 .0256 .0250 .0322 .0314 0401 0392 .0485 0606 .0594 .0721 0885 .0869 .1056 1920 .1038 404 .1251 4990 .1230 20 .1469 .1446 Tror .1711 1685 404 1040 .1977 .1949 20 var 2266 .2236 .2578 .2546 .2912 2877 .3264 .3228 .3632 .3594 4013 .3974 .4404 .4364 .4801 .4761 .0099 .0129 .0166 .0212 ,0268 .0336 0418 .0516 0630 .0764 ,0918 .1093 420 .1292 are .1515 .1762 10 .2033 2007 .2327 .2643 .2981 .3336 3707 .4090 .4483 .0003 .0004 .0005 .0007 .0010 .0014 .0020 .0027 .0037 .0049 .0066 .0087 .0113 .0146 .0188 .0239 .0301 .0375 .0465 0571 .0694 .0838 1002 . 1003 4400 .1190 41 .1401 .1635 .1894 .2177 .2483 .2810 3156 .3520 .3897 .4286 4681 0495 .0002 .0003 .0005 .0007 .0010 .0014 .0019 .0026 .0036 .0048 .0064 .0084 .01 10 .0143 .0183 10) .0233 0294 0294 .0367 .0455 .0559 .0681 .0823 0985 .0985 .1170 4975 . 1379 .1611 2005 .1867 .2148 .2451 .2776 .3121 .3483 .3859 .4247 .4641 0735 .0307 .0384 .0475 ,0582 .0708 .0853 . 1020 .1210 * .1423 .1660 . 1922 02 .2206 co .2514 .2843 .3192 .3557 .3936 4325 .4721 .0537 0655 .0793 ,0951 .1131 4990 .1335 .1562 2012 .1814 .2090 .2389 .2709 .3050 .3409 .3783 .4168 4562 4960 .4880 A project designed to refurbish a hospital operating theatre consists of activities A,B,C,D,E F, G and ,H, The estimated times (optimistic, most-likely and pessimistic times) and precedence relationships shown are as shown. Activity Immediate Optimistic Most Likely Pessimistic Predecessor Time (0) Time (M) Time (P) S A 5 6 7 . A 10 13 28 A 1 2 15 1 D A 8 9 16 E B 25 36 41 F. B,C,D 6 9 18 G D 7 12 17 H E,F,G 12 15 24 Standard Normal Probabilities Table entry Table entry for z is the area under the standard normal curve to the left of z. Z .00 .01 .02 .03 .05 .06 .07 .08 .09 .0003 .0005 .0007 .0009 .0013 .0018 .0025 .0034 .0045 .0060 .0080 .0104 .0136 .0174 ,0222 0222 .0281 0201 .0351 ,0003 .0004 .0006 .0009 .0012 .0017 .0023 .0032 .0043 .0057 , .0003 .0004 .0005 .0008 .0011 .0015 .0021 .0028 .0038 .0051 .0068 .0089 .0116 .0150 .0192 .0054 .0075 .0244 -3.4 -3.3 -3.2 -3.1 -3.0 -2.9 -2.8 -2.7 -2.6 -2.5 -2.4 -2.3 -2.2 -2.1 -2.0 -1.9 -1.8 -1.7 -1.6 -1.5 -1.4 42 -1.3 -1.2 -1.1 -1.0 0.9 -0.8 -0.7 2 -0.6 -0.5 -0.4 -0.3 -0.2 0.1 -0.0 .0003 .0005 .0007 .0010 .0013 .0019 .0026 .0035 .0047 .0062 .0082 .0107 .0139 .0179 .0228 0228 .0287 .0359 .0446 .0548 .0668 .0808 POCO .0968 we .1151 .1357 20 .1587 .1841 2119 .2420 2743 .3085 .3446 .3821 .4207 4602 .5000 .0003 .0005 .0006 .0009 .0013 .0018 .0024 0033 .0044 .0059 .0078 .0102 .0132 0170 .0217 .0274 .0344 0427 0526 .0643 0779 .0778 02 .0934 4444 .1112 2014 .1314 .1539 1200 .1788 2061 .2358 2676 .3015 .3372 .3745 4129 4522 4920 .0436 .04 .0003 .0004 .0006 .0008 .0012 .0016 .0023 .0031 .0041 .0055 .0073 .0096 .0125 .0162 .0207 .0262 .0329 0409 .0505 0618 .0749 .0901 076 .1075 1024 .1271 4400 .1492 1534 .1736 .2005 .2296 2611 .2946 .3300 .3669 .4052 .4443 .4840 .0003 .0003 .0004 .0004 0006 0006 ,0008 .0008 .0011 .0011 .0016 .0015 .0022 .0021 .0030 .0029 0040 .0039 .0052 .0071 .0069 .0094 .0091 0122 .0119 .0158 .0154 .0202 .0197 .0256 .0250 .0322 .0314 0401 0392 .0485 0606 .0594 .0721 0885 .0869 .1056 1920 .1038 404 .1251 4990 .1230 20 .1469 .1446 Tror .1711 1685 404 1040 .1977 .1949 20 var 2266 .2236 .2578 .2546 .2912 2877 .3264 .3228 .3632 .3594 4013 .3974 .4404 .4364 .4801 .4761 .0099 .0129 .0166 .0212 ,0268 .0336 0418 .0516 0630 .0764 ,0918 .1093 420 .1292 are .1515 .1762 10 .2033 2007 .2327 .2643 .2981 .3336 3707 .4090 .4483 .0003 .0004 .0005 .0007 .0010 .0014 .0020 .0027 .0037 .0049 .0066 .0087 .0113 .0146 .0188 .0239 .0301 .0375 .0465 0571 .0694 .0838 1002 . 1003 4400 .1190 41 .1401 .1635 .1894 .2177 .2483 .2810 3156 .3520 .3897 .4286 4681 0495 .0002 .0003 .0005 .0007 .0010 .0014 .0019 .0026 .0036 .0048 .0064 .0084 .01 10 .0143 .0183 10) .0233 0294 0294 .0367 .0455 .0559 .0681 .0823 0985 .0985 .1170 4975 . 1379 .1611 2005 .1867 .2148 .2451 .2776 .3121 .3483 .3859 .4247 .4641 0735 .0307 .0384 .0475 ,0582 .0708 .0853 . 1020 .1210 * .1423 .1660 . 1922 02 .2206 co .2514 .2843 .3192 .3557 .3936 4325 .4721 .0537 0655 .0793 ,0951 .1131 4990 .1335 .1562 2012 .1814 .2090 .2389 .2709 .3050 .3409 .3783 .4168 4562 4960 .4880
