Question: Two brothers have purchased a small lot, in the center of town, where they intend to build a gas station. The station will have two pumps, a service area for water and tire maintenance, and a main building with restrooms, office, and cash register area. Before they begin excavating the site, the local authorities must approve the location for a gasoline station and be certain that the placement of the storage tanks will not interfere with water, gas, and electric lines that are already in place. Once the site has been approved, the excavation can begin. After excavation, the three primary parts of the construction can begin: laying in the gasoline tanks, building the water and tire service area (including installation of the air compressor), and constructing the main building. The surfacing can begin after all building is completed. After surfacing, the site must be cleaned and the station's signs erected. However, before the station can open for business, the air compressor must be inspected, tested, and approved. The activities and the time required for each of them are as follows:

a. Based on the description of the project, determine the activity precedence relationships and develop a network for the project.

b. Determine the critical path and the earliest and the latest starting and finishing times for each activity.

c. Draw the Gantt chart for this project based on earliest times.

d. Suppose that the air compressor fails to function correctly and must be replaced. It takes two weeks to obtain another compressor and test it. Will the project necessarily be delayed as a result?

e. List the activities that must be completed by the end of the 15th week in order to guarantee that the project is not delayed.

f. Solve this problem using linear programming.