Consider the following network

The optimistic time, most likely time and pessimistic time of all the activities are given in the table below :

The standard deviation of the critical path is

Consider the following Linear Programming problem $$(LLP)$$

Maximize: $$Z = 3{x_1} + 2{x_2}$$
$$\,\,$$ Subject $$\,\,$$ to
$$\eqalign{ & \,\,\,\,\,\,\,{x_1} \le 4 \cr & \,\,\,\,\,\,\,{x_2} \le 6 \cr & 3{x_1} + 2{x_2} \le 18 \cr & {x_1} \ge 0,\,\,{x_2} \ge 0 \cr} $$

Six jobs arrived in a sequence as given below:

Average flow time (in days) for the above jobs using Shortest Processing Time rule is

A $${20^ \circ }$$ full depth involute spur pinion of $$4mm$$ module and $$21$$ teeth is to transmit $$15kW$$ at $$960rpm.$$ Its face width is $$25mm.$$

Given that the tooth geometry factor is $$0.32$$ and the combined effect of dynamic load and allied factors intensifying the stress is $$1.5;$$ the minimum allowable stress (in $$MPa$$) for the gear material is