# Question

Good Homes Construction Company is about to begin the construction of a large new home. The company’s president, Michael Dean, is currently planning the schedule for this project. Michael has identified the five major activities (labeled A, B, . . . , E) that will need to be performed according to the project network shown next, followed by a table giving the normal point and crash point for each of these activities.

These costs reflect the company’s direct costs for the material, equipment, and direct labor required to perform the activities. In addition, the company incurs indirect project costs such as supervision and other customary overhead costs, interest charges for capital tied up, and so forth. Michael estimates that these indirect costs run $5,000 per week. He wants to minimize the overall cost of the project. Therefore, to save some of these indirect costs, Michael concludes that he should shorten the project by doing some crashing to the extent that the crashing cost for each additional week saved is less than $5,000.

(a) Use marginal cost analysis to determine which activities should be crashed and by how much to minimize the overall cost of the project. Under this plan, what is the duration and cost of each activity? How much money is saved by doing this crashing?

(b) Now use the linear programming approach to do part (a) by shortening the deadline 1 week at a time.

These costs reflect the company’s direct costs for the material, equipment, and direct labor required to perform the activities. In addition, the company incurs indirect project costs such as supervision and other customary overhead costs, interest charges for capital tied up, and so forth. Michael estimates that these indirect costs run $5,000 per week. He wants to minimize the overall cost of the project. Therefore, to save some of these indirect costs, Michael concludes that he should shorten the project by doing some crashing to the extent that the crashing cost for each additional week saved is less than $5,000.

(a) Use marginal cost analysis to determine which activities should be crashed and by how much to minimize the overall cost of the project. Under this plan, what is the duration and cost of each activity? How much money is saved by doing this crashing?

(b) Now use the linear programming approach to do part (a) by shortening the deadline 1 week at a time.

## Answer to relevant Questions

The 21st Century Studios is about to begin the production of its most important (and most expensive) movie of the year. The movie’s producer, Dusty Hoffmer, has decided to use PERT/CPM to help plan and control this key ...Use the algorithm described in Sec. 10.3 to find the shortest path through each of the following networks, where the numbers represent actual distances between the corresponding nodes. (a) (b) Consider the following integer nonlinear programming problem. Maximize Z = 18x1 – x21 + 20x2 + 10x3, Subject to 2x1 + 4x2 + 3x3 ≤ 11 and x1, x2, x3 are nonnegative integers. Use dynamic programming to solve this problem. The owner of a chain of three grocery stores has purchased five crates of fresh strawberries. The estimated probability distribution of potential sales of the strawberries before spoilage differs among the three stores. ...Consider the following project network (as described in Sec. 10.8), where the number over each node is the time required for the corresponding activity. Consider the problem of finding the longest path (the largest total ...Post your question

0