Question: A construction company is about to begin construction on a large hoMeand has identified five major activities (labeled A, B, C, D, and E) that will need to be performed according to the following project network. Also shown are each activity’s normal duration (in weeks) and cost (direct costs for the material, equipment, and direct labor). In addition, the company incurs indirect project costs, such as supervision and overhead, which are estimated to be $5000 per week. The manager wants to minimize the overall cost of the project. To save indirect costs, the manager will consider shortening the length of the project by crashing as long as the crashing costs for each week saved is less than $5000. Included in the table below are: a compressed tiMeand weekly compression cost for each activity. The compressed time is a new, shorter activity duration for which the additional cost is incurred (the weekly compression cost). For example. Activity A can be done in 3 weeks for a cost of $54,000 or in 2 weeks at a cost of $60,000 ($54,000+$6,000). For each activity, assume that costs to crash per week are linear and that you can opt to reduce its time by all or part of the possible reduction. This means that, for example, on activity C normal time is 5 and compressed time is 2 so that you may opt to crash C down to 4, 3 or 2 weeks, with additional cost of $1,333 for each week saved.

a. List all paths. Which is the critical path and what is project length, assuming normal activity times?

b.

Determine which activities to crash, and by how much and in what order, to minimize the overall cost of the project. Show clearly the steps of your crashing decisions (in order). Under your crashing plan, what is the project duration and what activities are critical?