In a forecasting model, at the end of period $$13,$$ the forecasted value for period $$14$$ is $$75.$$ Actual value in the periods $$14$$ to $$16$$ are constant at $$100$$. if the assumed simple exponential smoothing parameter is $$0.5,$$ then the $$MSE$$ at the end of period $$16$$ is

The cost of providing service in a queuing system increases with

People arrive at a hotel in a Poisson distributed arrival rate of $$8$$ per hour. Service time distribution is closely approximated by the negative exponential. The average service time is $$5$$ minutes. Calculate (a) the mean number in the waiting line; (b) the mean number in the system; (c) the waiting time in the queue; (d) the mean time in the system, and (e) the utilization factor.

A company rents three warehouses $$A, B$$ and $$C$$ from which they supply bearings to two customers $$P$$ and $$Q.$$ The profit per piece, the annual demands of the customers and the supplies available from the warehouses are shown below:

As the company is not able to meet the demands, it is proposed to replace warehouse $$C$$ with a warehouse rented at $$D$$ whose supply capacity would be $$5000.$$ The expected profit would be Rs.$$6$$ and Rs.$$5$$ per piece distributed to $$P$$ and $$Q$$ respectively. The rental charges for warehouse $$D$$ is Rs.$$5,000$$ per year. Find the increase in the profit of the company after replacing warehouse $$C$$ by $$D.$$