$title Brick design  (BRICK,SEQ=437)
$ontext

The task: design a brick s.t.
  1. The base has an area of at least A square units
  2. The volume is at least V cubic units
  3. Length, width, and height are at least L, W, and H
  4. The length and/or width will be fixed: this trumps L or W or A

This contrived example serves to illustrate how varlist matching
can be useful in MCP models.

It's helpful to the solver to use positive minimum dimensions.
$offtext

* minimum dims for our brick
scalars
  L  'min length' / 0.5 /
  W  'min width'  / 0.5 /
  H  'min height' / 0.5 /
  A  'min area'   / 10 /
  V  'min volume' / 30 /
  ;
variables
  xL / LO [L] /
  xW / LO [W] /
  xH / LO [H] /
  ;
equations
  Areq   'meet area requirement'
  Vreq   'meet volume requirement'
  ;

Areq ..  xL * xW =N= A;
Vreq ..  xL * xW * xH =N= V;

model m / Vreq.xH, Areq : (xL|xW) /;

xL.fx = 5;
solve m using mcp;

* fixing both xL and xW essentially removes the area constraint
xW.fx = 3;
solve m using mcp;