Solve the following LPP. Maximize Z = 2 x₁ + 5x₂ subject to the conditions x₁+ 4x₂ ≤ 24. 3x₁+x₂ ≤ 21, x₁+x₂ ≤ 9 and x₁, x₂ ≥ 0.

Solve the following LPP.
Maximize Z= 2 x₁ + 3x₂ subject to constraints x₁ + x₂ ≤ 30; x₂ ≤ 12; x₁ ≤ 20 and x₁, x₂ ≥ 0.

A company manufactures two models of voltage stabilizers viz., ordinary and autocut. All components of the stabilizers are purchased from outside sources, assembly and testing is carried out at company’s own works. The assembly and testing time required for the two models are 0.8 hour each for ordinary and 1.20 hours each for auto-cut. Manufacturing capacity 720 hours at present is available per week. The market for the two models has been surveyed which suggests maximum weekly sale of 600 units of ordinary and 400 units of auto-cut. Profit per unit for ordinary and auto-cut models has been estimated at Rs. 100 and Rs. 150 respectively. Formulate the linear programming problem.

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

A project schedule has the following characteristics

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.