Suppose that, in addition to edge capacities, a flow network has vertex capacities. that is each vertex vv has a limit l(v)l(v) on how much flow can pass though vv. show how to transform a flow network g = (v, e)g=(v, e) with vertex capacities into an equivalent flow network g' = (v', e')g ′ =(v ′ ,e ′ ) without vertex capacities, such that a maximum flow in g'g ′ has the same value as a maximum flow in gg. how many vertices and edges does g'g ′ have?

:you areto design the controller for alight that functions both as an ordinary light and also as a motion activated light and alarm. a.if the manual switch s is on, then the light l is on. b.besides the manual switch, there is a motion detector, m1, which activatesthis light.c.if motion is detected but the light is on anyway because s is on, only then a secondoutput a, an alarm, is turned on. d.the disable switch, d, disables the motion activated light and alarmbut leaves manual control operation of the light using switch s.(i)read the problem statement and clearly identify the inputs and outputs for the circuit you are designing. (ii)create the truth table for this system; include the light, alarm, switch, disable, and the motion sensor.(iii)draw a schematic of this system.

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