set PEOPLE;
set PROJECTS;

set ABILITIES within (PEOPLE cross PROJECTS);

param supply {PEOPLE} >= 0;   # hours each person is available
param demand {PROJECTS} >= 0; # hours each project requires

check: sum {i in PEOPLE} supply[i] = sum {j in PROJECTS} demand[j];

param cost {ABILITIES} >= 0;   # cost per hour of work
param limit {ABILITIES} >= 0;  # maximum contributions to projects

var Assign {(i,j) in ABILITIES} >= 0, <= limit[i,j];

minimize Total_Cost:
   sum {(i,j) in ABILITIES} cost[i,j] * Assign[i,j];

subject to Supply {i in PEOPLE}:
   sum {(i,j) in ABILITIES} Assign[i,j] = supply[i];

subject to Demand {j in PROJECTS}:
   sum {(i,j) in ABILITIES} Assign[i,j] = demand[j];