Q1. Describe the concept of cycling and degeneracy in the linear programming problems.
Q2. Solve the given LPP by using the graphical method:
Minimize Z = 20X1 + 40X2
Subject to constraints
36X1 + 6X2 ≥ 108
3X1 + 12X2 ≥ 36
20X1 + 10X2 ≥ 100
X1, X2 ≥ 0 (14)
Q3. Write down the Dual of the given LPP
Minimize Z = 4X1 + 5X2- 3X3
Subject to constraints:
X1+ X2 + X3 = 22
3X1+ 5X2 - 2X3 < 65
X1+ 7X2 +4X3 > 120
X1, X2 > 0 and X3 is unrestricted
Q4. The given table gives the machining times in hours for five machines for performing five jobs. Each and every machine can be assigned to just one machine. Solve this as an assignment problem with an objective to minimize the net time.
