Math Problem Statement

Because you have to be back to school in September, and you cannot start before you have finished your last final exam l, you need to shorten the project to 63 days ( end of June to end of August). You want to keep the cost as low as possible since the budget is very tight. What is the minimum total cost to finish the project in 63 days?

Solution

To minimize the total cost to complete the project in 63 days, we need to consider the normal duration and cost of each task, along with any available options for crashing the tasks (reducing their duration at an extra cost). By strategically crashing specific tasks, we can shorten the project to meet the 63-day requirement while minimizing the additional cost.

Here is a structured approach to solve the problem:

  1. Identify the Critical Path: The critical path is the longest path in the project network and determines the minimum time in which the project can be completed. To reduce the project duration to 63 days, we will need to shorten the activities along this path.

  2. Analyze Crash Costs: For each activity on the critical path, examine the crash costs, which represent the additional cost per day to reduce the activity's duration. Identify the activities with the lowest crash costs on the critical path since they will be the most cost-effective to shorten.

  3. Crash Activities Incrementally: Start by crashing the lowest-cost activities on the critical path and continue until the project duration is reduced to 63 days. Ensure that crashing does not change the critical path unnecessarily.

  4. Calculate the Total Cost: The minimum total cost will be the sum of the normal project cost plus the additional costs incurred by crashing the selected activities.

Please provide details on the specific activities, their normal durations, crash durations, and crash costs if available. This information is essential for calculating the exact minimum cost to complete the project in 63 days.

Would you like assistance setting up this calculation based on activity details, or do you have specific data on crashable activities?


Here are five questions to consider:

  1. What are the durations and normal costs of each activity?
  2. Which activities are part of the critical path?
  3. What are the crash costs per day for each critical path activity?
  4. Are there dependencies between activities that could affect the new critical path after crashing?
  5. What is the budget limit for this project?

Tip: Identifying the critical path before crashing any activities will save you from incurring unnecessary costs by focusing only on the tasks that impact the project's overall duration.

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Math Problem Analysis

Mathematical Concepts

Project Management
Critical Path Method
Cost Optimization

Formulas

Critical Path Duration = Sum of durations of activities on the critical path
Total Project Cost = Normal Cost + Crash Cost

Theorems

Critical Path Theorem
Cost Minimization Strategy

Suitable Grade Level

Grades 11-12 / College