Solve graphically: Minimize Z = 20x₁ + 40x_2.
Subject to the constraints 36x₁ + 6x₂ ≥ 108,3x₁ + 12x₂ ≥ 36,20x₁ + 10x₂ ≥ 100 and x₁,x₂≥0

Minimize and maximize Z =x₁+ 2x₂ . Subject to the constraints x₁ + 2x₂ ≥ 100,2x₁ − x₂ ≤ 0,2x₁ + x₂ ≤ 200 and x₁,x₂ ≥ 10.

Compute the earliest start time, earliest finish time, latest start time and latest finish time of each activity of the project given below:

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

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)	7	6	11	3	9	2	4	9	6	3

 

The following table use the activities in a building project.

Activity	1-2	1-3	2-3	2-4	3-4	4-5
Duration (days)	21	26	11	13	5	11

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.