A Project has the following time schedule

Activity	1-2	1-6	2-3	2-4	3-5	4-5	6-7	5-8	7-8
Duration(in days)	7	6	14	5	11	7	11	4	18

Construct the network and calculate the earliest start time, earliest finish time, latest start time and latest finish time of each activity and determine the Critical path of the project and duration to complete the project.

Calculate the earliest start time, earliest finish time, latest start time and latest finish time of each activity of the project given below and determine the Critical path of the project and duration to complete the project.

Activity	1-2	1-3	1-5	2-3	2-4	3-4	3-5	3-6	4-6	5-6
Duration ( in week)	8	7	12	4	10	3	5	10	7	4

Solve the following linear programming problem graphically.
Minimize Z = 200x₁+ 500x₂ subject to the constraints x₁+2x₂ ≥ 10; 3x₁+4x₂ ≤ 24 and x₁ ≥ 0, x₂ ≥ 0

Solve the following linear programming problem graphically. Maximize Z = 60x₁ + 15x₂ subject to the constraints: x₁ + x₂ ≤ 50; 3x₁ + x₂ ≤ 90 and x₁, x₂ ≥ 0.

The following table gives the characteristics of project

Activity	1-2	1-3	2-3	3-4	3-5	4-6	5-6	6-7
Duration (in days)	5	10	3	4	6	6	5	5

Draw the network for the project, calculate the earliest start time, earliest finish time, latest start time and latest finish time of each activity and find the critical path. Compute the project duration.