The standard deviation of linear dimensions $$P$$ and $$Q$$ are $$3\mu m$$ and $$4\mu m$$, respectively. When assembled, the standard deviation (in $$\mu m$$) of the following linear dimension $$(P+Q)$$ is ___________.

For a single server with Poisson arrival and exponential service time, the arrival rate is $$12$$ per hour. Which one of the following service rates will provide a steady state finite queue length?

A project starts with activity $$A$$ and ends with activity $$F.$$ The precedence relation and durations of the activities are as per the following table:

The minimum project completion time (in days) is ___________

A product made in two factories $$P$$ and $$Q,$$ is transported to two destinations, $$R$$ and $$S.$$ The per unit costs of transportation (in Rupees) from factories to destinations are as per the following matrix.

Factory $$P$$ produces $$7$$ units and factory $$Q$$ produces $$9$$ units of the product. Each destination requires $$8$$ units. If the north-west corner method provides the total transportation cost as $$X$$ (in Rupees) and the optimized (the minimum) total transportation cost $$Y$$ (in Rupees), then $$(X$$-$$Y),$$ in Rupees, is