3. At a signal-controlled intersection, a two-way road meets three one-way roads (see figure below). Permitted turning movements a, & co and : can be paired off for greens by the phasing of traffic lights. The average flow of vehicles for each turn is given in the following table 7 24 10 30 5 and the possible phasings (i.e., pairs of lights that turn green at the same time) are: a and &, d and e, a and & & and c, and & and a. Find out what proportion of green time should be given to the various phasings such that the smallest average number of vehicles allowed through on a green phase through a, &, c d or : is as large as possible. b. Is the solution unique? If it is not unique find another solution