The sales of a product during the last four years were $$860, 880, 870$$ and $$890$$ units. The forecast for the fourth year was $$876$$ units. If the forecast for the fifth year, using simple exponential smoothing, is equal to the forecast using a three period moving average, the value of the exponential smoothing constant $$\alpha $$ is

A project has six activities $$(A$$ to $$F)$$ with respective activity durations $$7,5,6,6,8,4$$ days. The network has three paths $$A-B,C-D$$ and $$E-F.$$ All the activities can be crashed with the same crash cost per day. The number of activities that need to be crashed to reduce the project duration by $$1$$ day is

The distribution of lead-time demand fro an item is as follows:

The reorder level is $$1.25$$ times the expected value of the lead-time demand. The service level is

A band brake consists of a lever attached to one end of the band. The other end of the band is fixed to the ground. The wheel has a radius of $$200$$ $$mm$$ and the wrap angle of the band is $${270^ \circ }$$. The braking force applied to the lever is limited to $$100N,$$ and the coefficient of friction between the band and the wheel is $$0.5.$$ No other information is given.

The maximum wheel torque that can be completely braked is