Build the following block layout model. The total available area can be described as

a rectangle of length $120$m by width $80$m$.$ Where, the bottom left place of size $20$m by $20$m is

reserved for passage to the underground parking. There are four departments in total, and in

general, the aspect ratio for all the departments should be $1\mathrm{.}1.$ However, Department $3$ must be

square in shape. The upper and lower limits for both length and width are $10$m and $70$m$.$ The upper

and lower limits for any department$$s perimeter is $120$m and $200$m$.$ The cost per unit flow is $$1$

between any two departments. The flow matrix per day between the departments as given in the

following matrix. Assume any missing information, and develop an optimal block layou