Floorplanning

Consider the apartment floorplan shown in the table below. The problem is to find the length and width of each room that will minimize the cost of the apartment, subject to some constraints. The cost for each room in this case is the area except for the cost of the kitchen and bathroom, whose costs are twice their respective areas. The constraints are:

Length Width Area
Room Min Max Min Max Min Max Proportion
Living 8 20 8 20 120 300 1.5
Kitchen 6 18 6 18 50 120 Any
Bath 5.5 5.5 8.5 8.5
Hall 5.5 5.5 3.5 6 19 72 Any
Bed1 10 17 10 17 100 180 1.5
Bed2 9 20 9 20 100 180 1.5
Bed3 8 18 8 18 100 180 1.5
Further, there must be a space -- 3.0 units -- for a doorway in the walls connecting bed2 and bed3 to the hall, and all rooms are rectangular (as is the entire plan).

Good Luck