the following table shows the distances between different cities

C$0$ C$1$ C$2$ C$3$

C$00\mathrm{.}0054\mathrm{.}0050\mathrm{.}0040\mathrm{.}00$

C$154\mathrm{.}000\mathrm{.}0025\mathrm{.}0023\mathrm{.}00$

C$250\mathrm{.}0025\mathrm{.}000\mathrm{.}0011\mathrm{.}00$

C$340\mathrm{.}0023\mathrm{.}0011\mathrm{.}000\mathrm{.}00$

$[$Distance of $0$ means distance is not applicable.

$]$The following table shows the pheromone in units between different cities

C$0$ C$1$ C$2$ C$3$

C$00\mathrm{.}000\mathrm{.}0033\mathrm{.}4712\mathrm{.}90$

C$10\mathrm{.}000\mathrm{.}0042\mathrm{.}4521\mathrm{.}63$

C$233\mathrm{.}4742\mathrm{.}450\mathrm{.}0015\mathrm{.}30$

C$312\mathrm{.}9021\mathrm{.}6315\mathrm{.}300\mathrm{.}00$

$$ Assume that an ant has followed the following route:$[0,3,1,2,]$ and back to source

a$.$ Calculate the total cost of the above route.

b$.$ Calculate the ant's switching probabilities for the first $1$ steps in the above route assuming pheromone exponent parameter $\backslash$alpha $=0\mathrm{.}62$ and heuristic exponent parameter $\backslash$beta $=0\mathrm{.}40.$

c$.$ Calculate the updated pheromone amounts after applying the ACO evaporation step assuming $\backslash$rho $=0\mathrm{.}36.$

d$.$ Calculate the updated pheromone amounts after applying the ACO depositing step assuming Q$=25\mathrm{.}86.$