1. Solve the following LP-Problem through simplex method
MAX. Z = 10x1 + 5x2
Subject to
4x1 + 5x2 ≥ 100
5x1 + 2x2 ≥ 80
x1, xz ≥ 0
2. a) Write the DUAL of the problem given in Question No.1.
b) Explain the conceptual differences between PRIMAL and DUAL
c) Explain the significance of shadow price
2. An item is produced at the rate of 50 items per day and is consumed at the rate of 25 items per day. If the set up cost is Rs.100 per production run and holding cost in stock is Re.0.01 per unit of item per day. Find the economic lot size and the run length.
3. In a bank there is only one window. A solitary employee performs
all the services required and the window remains continuously open
from 7.am to 1 pm. It has been discovered that the average number
of clients are 54 during the day and the average service time is of
five minutes per person. Calculate
i) Average number of clients in the system
ii) Average waiting time in the queue
iii) Utilisation rate of the employee
4. Write short note on any three of the following
a) Dynamic Programming
b) GOAL Programming
c) Simulation
d) Saddle point, Pure and Mixed Strategy
e) Degeneracy in Transportation Problem