1) Demand for the computer monitor cable is 1050 cables/month and shortages are approved. If cost per cable is Rs.125, cost of making one purchase is: Rs.700, holding cost of one cable is: Rs.3 per year and cost of one shortage is: Rs.50 per year. Find out optimum total yearly cost, optimum purchase quantity, number of orders per year, optimum number of shortages, time between order and maximum inventing.
2) The automobile service centre has three same service points each of which can service the average of 5 automobile per hour. Average of 10 automobiles enters each hr at service centre. Arrivals are Poisson and service is exponentially distributed with parking facilities being unlimited.
Find out:
(a) Expected number of automobile in the system
(b) Expected time spent by an automobile waiting for service
(c) Expected time of an automobile spent in the system.
3) Deduce the optimal solution from Kuhn-Tucker conditions for problem given below.
Minimize Z = 2x1 + 3x2 – x12 – 2x22
Subjected to x1 + 3x2 ≤ 6
5x1 + 2x2 ≤ 10 and x1 ≥ 0 , x2 ≥ 0
4) Explain Interval halving method with suitable examples.
5) Write down the steps which are involved in system analysis and Design? Describe in detail.
6) Machine shop has 20 CNC Machines each with one operator. As idle time of these machines costly, concern has 4 reserve operators to drive the machines when some usual operators are absent. If the operator is not available the machine will be unoccupied. Number of operators who are absent daily is explained by probability distribution which is given below:
No. Absent 0 1 2 3 4 5 6 7
Probability 0.05 0.15 0.20 0.22 0.1 0.08 0.10 .10
Determine the following using Monte Carlo simulation method.
(i) Consumption of reserve operators
(ii) Probability that at least one CNC machine will be idle due to non availability of the operator.
Explain the answers of the questions given above.