Develop a linear programming model to estimate the minimum project duration for the network shown below if the numbers on the arcs are activity numbers and normal activity times are given in the table. 6 Normal Activity Time 1 10 2 8 3 4 10 5 5345 6 6 7 5 8 6 9 6 10 4
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- Consider a project that has been modeled as in Table 1 Draw the PERT/CPM network for this project and determine the project’s expected completion time µP and its critical path. Suppose the standard deviations of the activity durations are σA = 2, σB = 1, σC = 0, σD = 2, σE = 3, and σF = 0. Then please estimate the standard deviation of the overall project’s standard deviation σP . Suppose for the standard Normal random variable Z, we know P[−1 ≤ Z ≤ +1] ' 68%, P[−2 ≤ Z ≤ +2] ' 95%, and P[−3 ≤ Z ≤ +3] ' 99.7%. Then, approximately what time T is one for which there is only a less than 2.5% chance for the completion time to beat (be shorter than)?An IT project manager of ABC Company has developed an activity list for the purpose oftracking employees’ daily activities on the project. The project’s schedule is considered to be ofhigh risk due to the possibility of sabotage by some of the employees. In addition, the IT projectmanager has gathered time information for each activity, as shown in the table below. Considerthe following project’s tasks and their identified best, likely, and worst case estimates of taskduration. Assume the organization computes PERT weight average based on the standardformula.Activity Optimistic MostlikelyPessimisticA 5 5 25B 3 5 8C 7 5 8D 4 4 5E 10 19 34F 3 14 18G 6 16 20H 32 44 65I 12 17 25J 2 8 18The dependencies between the 10 activities listed in the table above are as follows: The project starts with two activities—A, and B—which can be done concurrently. When activity A is finished, activity C can start When activity B is finished, activities D and E can start When both activities C and D are…What is the minimum cost of crashing the following project that Roger Solano manages at Slippery Rock University by 4 days? Normal Crash Activity Time (days) Time (days) A B C D E 580 4 (O ∞ 6 8 4 6 3 4 5 Normal Cost Activity A B C D E $800 $200 $600 $750 $1,200 Total Cost with Crashing Immediate Predecessor(s) $1,100 $500 $650 The total cost of crashing the project by 4 days is $ $1,500 $1,650 By how many days should each activity be crashed to reduce the project completion time by 4 days? Fill in the tab below. (Enter your responses as whole numbers.) Each Activity Should be Reduced BY (days) 1 0 1 2 3 | | | < 0 (Enter your response as a whole number.)
- The Advanced Tech Company has a project to design an integrated information data base for a major bank. Data for the project are given in the following table. Indirect project costs amount to $250 per day. The company will incur a $200 per day penalty for each day the project lasts beyond day 12. Activity Normal Time (days) Normal Cost ($) Crash Time (days) Crash Cost ($) Immediate Predecessor(s) A 5 800 4 1,000 − B 5 1,100 2 2,900 − C 2 600 1 900 A, B D 3 1,200 2 2,000 B E 3 1,500 2 1,700 C, D F 2 1,300 1 1,400 E G 3 900 3 900 E H 5 500 2 800 G a. What is the project's duration if only normal times are used? The project duration is nothing day(s). (Enter your response as an integer.)…Your hospital has applied for certification as a level 1 stroke center. It is critical that the following project is completed in 18 weeks, before the next Joint Commission survey. Project activity times are listed in the table attached as an image. Determine the minimum cost-schedule for this project to be completed in 18 weeks. Assume a linear relationship between crash cost and crash time. For example, crash cost per week for activity A can be calculated as: ($650 - $200)/(4-2) = $225. 2. What is the difference in total project costs between the earliest completion time of the project using normal times and the minimum cost-schedule you found in part 1?What is the minimum cost of crashing the following project that Roger Solano manages at Slippery Rock University by 4 days? Crash Normal Activity Time (days) Time (days) Normal Cost A 6 5 $800 B 7 5 $200 с 4 3 $600 D 5 2 $750 E 6 4 $1,200 The total cost of crashing the project by 4 days is $ Activity A B с D E Total Cost with Crashing Immediate Predecessor(s) By how many days should each activity be crashed to reduce the project completion time by 4 days? Fill in the table below. (Enter your responses as whole numbers.) Each Activity Should be Reduced BY (days) (Enter your response as a whole number.) $1,100 $500 $650 $1,500 $1,650 ☐☐☐☐☐ A с
- What is the minimum cost of crashing the following project that Roger Solano manages at Slippery Rock University by 4 days? Normal Crash Time Activity Time (days) (days) AB А C D E 67555 5 BCD w 55 с 4 2 Activity A E 3 Normal Cost $800 $300 $600 $750 $1,200 Immediate Total Cost with Crashing Predecessor(s) $1,100 $500 By how many days should each activity be crashed to reduce the project completion time by 4 days? Fill in the table below. (Enter your responses as whole numbers.) $650 $1,500 $1,650 - Each Activity Should be Reduced BY (days) A CWhat is the minimum cost of crashing the following project that Roger Solano manages at Slippery Rock University by 4 days? Crash Normal Activity Time (days) Time (days) Normal Cost A 5 4 B 9 7 C 6 5 D 7 5 E 7 4 Total Cost with Crashing Immediate Predecessor(s) $800 $300 $600 $750 $1,200 By how many days should each activity be crashed to reduce the project completion time by 4 days? Fill in the table below. (Enter your responses as whole numbers.) Each Activity Should be Reduced BY (days) Activity A B C D E $1,100 $400 $650 $1,500 $1,650 | | | < 0The table below contains data for the installation of new equipment in a manufacturing process for a steel corporation. Your company is responsible for the installation project. Indirect costs are $6,000 per week, and a penalty cost of $10,000 per week will be incurred by your company for every week the project is delayed beyond week 15. Activity Immediate Predecessor(s) Normal Time (weeks) Crash Time (weeks) Normal Cost ($) Crash Cost ($) A None 2 1 7,000 10,000 B None 2 2 3,000 3,000 C A 3 1 12,000 40,000 D B 3 2 12,000 28,000 E C 1 1 8,000 8,000 F D, E 5 3 5,000 15,000 G E 3 2 9,000 18,000 H F, G 8 6 14,000 32,000 Construct a network diagram for the project. What are the project completion time and the total cost under normal conditions? What is the shortest time duration for this project regardless of cost? What is the resulting total cost? What is the…
- The table below shows the duration and direct costs for the activities of a construction project. It is required to calculate the duration of the project that achieves the lowest possible total cost using the technique of crashing if the indirect costs are 5000$ per week. TITTI Activity Normal Time Normal Cost (NC) $ 6000 Crash Cost (CC) $ 12000 5000 Crash Time (NT) Weeks (CT) Weeks A 3 B 5 3000 2000 3 3 4000 6. 3000 3 6000 6. 9000 24000 Total Direct 23000 CostScott and Associates, Inc., is accounting firm that has three new clients. Project leaders will be assigned to the three clients. Based on the different backgrounds and experiences of the leaders, the various leader- client assignments differ in terms of projected completing times. The possible assignments and the estimated completion times in days are as follows: Client Project Leader 1 2 3 Abby 10 16 32 Bovi 14 22 40 Claire 22 24 34 Develop a network representation of this problem. Formulate the problem as a linear program.Please can you show me how this can be solved?