In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing constant must be close to

Customers arrive at a ticket counter at a rate of $$50$$ per hr and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is $$1$$ $$min.$$ Assuming that customer arrivals form a Poisson process and service times are exponentially distributed, the average waiting time in queue in $$min$$ is

A linear programming problem is shown below.
$$\eqalign{ & Maximize\,\,\,\,3x + 7y \cr & Subject\,\,to\,\,\,3x + 7y \le 10 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4x + 6y \le 8 \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x,\,\,y \ge 0 \cr} $$

It has ..............

A bar is subjected to fluctuating tensile load from $$20$$ $$kN$$ to $$100$$ $$kN.$$ The material has yield strength of $$240$$ $$MPa$$ and endurance limit in reversed bending is $$160$$ $$MPa.$$ According to the Soderberg principle, the area of cross-section in $$m{m^2}$$ of the bar for a factor of safety of $$2$$ is