Description

This problem designs the size of an L shaped house meeting
limitations imposed by city codes and aestheticconsiderations.

Small Model of Type : NLP

Category : GAMS Model library

Main file : house.gms

$title House Plan Design (HOUSE,SEQ=99)

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This problem designs the size of an L shaped house meeting
limitations imposed by city codes and aestheticconsiderations.


Borland, Eureka: The Solver. Tech. rep., Borland International, 1987.

Keywords: nonlinear programming, mathematics
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Variable
   x  'width of front wing         (ft)'
   y  'length of front wing        (ft)'
   z  'length of second story      (ft)'
   b  'total house width           (ft)'
   a  'length of back wing         (ft)'
   l  'total house length          (ft)'
   a1 'area of first floor      (sq ft)'
   a2 'area of the second floor (sq ft)'
   ta 'total area of the house  (sq ft)';

Equation
   defa1 'definition of first floor area  (sq ft)'
   defa2 'definition of second floor area (sq ft)'
   defta 'definition of total floor area  (sq ft)'
   defl  'definition of total house length   (ft)'
   minw  'front wing minimum width           (ft)'
   maxw  'front wing maximum width           (ft)'
   minp  'minimum pool area               (sq ft)'
   balk  'balcony size restriction           (ft)'
   prop  'wing proportionality               (ft)';

defa1.. a1 =e= x*y + a*b;

defa2.. a2 =e= x*z;

defta.. ta =e= a1 + a2;

minw..  x  =g= b/3;

maxw..  x  =l= b/2;

minp..  y*(b - x) =g= 1500;

defl..  l =e= y + a;

balk..  z =e= a + y/2;

prop..  a =g= y/2;

b.lo  =   40;
b.up  =   68;
l.lo  =   56;
l.up  =  100;
a1.up = 3000;

b.l = 68;
x.l = 30;

Model house / all /;

solve house maximizing ta using nlp;