A guidance and detection system is being built as part of a large defense project.

The detection portion consists of radar and sonar subsystems. Separate equipment is required for each of the subsystems. In each case, the equipment must be calibrated prior to production. After production, each subsystem is tested independently. The radar and the sonar are combined to form the detection system, which also must be tested prior to integration with the guidance system. The final test of the entire system requires complex equipment. The activities and the activity times are Activity Time Required (days)

A: Calibrate machine 1 (for radar) 2.0 B: Calibrate machine 2 (for sonar) 3.5 C: Calibrate machine 3 (for guidance) 1.5 D: Assemble and prepare final test gear 7.0 E: Make radar subsystem 4.5 F: Make sonar subsystem 5.0 G: Make guidance subsystem 4.5 H: Test radar subsystem 2.0 I: Test sonar subsystem 3.0 J: Test guidance subsystem 2.0 K: Assemble detection subsystem (radar and sonar) 1.5 L: Test detection subsystem 2.5 M: Final assembly of three systems 2.5 N: Testing of final assembly 3.5

a. Construct a network for this project.

b. Determine the earliest and the latest starting and finishing times for all the activities, and identify the critical path.

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

d. How much time is available for assembling and calibrating the final test gear without delaying the project?

e. What are the activities that must be completed by the end of 10 days to guarantee that the project is not delayed?

f. What are the activities that must be started by the end of 10 days to guarantee that the project is not delayed?

g. Solve this problem using linear programming.