A line balancing problem is solved in the context of

A manufacturing line requires $$7.2$$ minutes to make a product. The line has six workstations arranged as per the required sequence of operations. Total production required is $$300$$ products in $$7.5$$ hours. At steady state, the line efficiency, in $$\% $$, is ______________

Arrival of machines for repair in a maintenance shop follows a Poisson distribution at a rate of one per $$18$$ hours. The time to repair follows an exponential distribution with Mean Time To Repair $$(MTTR)$$ of $$14$$ hours. If the productivity loss is Rs.$$22,500$$ per hour, then the total expected loss of productivity due to machine breakdowns, in Rs., is

Two aluminium alloy plates each $$10$$ $$mm$$ thick and $$1$$ $$m$$ long are welded without crowning by multipass tungsten inert gas butt welding. The joint configuration is $$V$$-type with $${60^ \circ }$$ angle and root gap is maintained at $$5$$ $$mm.$$ If electrode of $$5$$ $$mm$$ diameter with $$500$$ $$mm$$ length is used for welding, then the number of electrodes required is