A solid cylinder (surface $$2$$) is located at the center of a hollow sphere (surface $$1$$). The diameter of the sphere is $$1m,$$ while the cylinder has a diameter and length of $$0.5m$$ each. The radiation configuration factor $${F_{11}}$$ is.

Hot oil is cooled from $${80^ \circ }C$$ to $${50^ \circ }C$$ in an oil cooler which uses air as the coolant. The air temperature rises from $${30^ \circ }C$$ to $${40^ \circ }C$$. the designer uses a $$LMTD$$ value of $${26^ \circ }C$$. the type of heat exchanger 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 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