Find the optimal solution(s) to this integer programming problem using a Microsoft Excel Solver. Interpret in words the solution.
Decision variables:
Xi= 1 if worker i is used, Xi= 0 if worker i is not used , for i=1,2,3,…,10
Yj = 1 if project j is undertaken , Yj = 0 otherwise , j=1,2,…,6
Objective function:
Max z= 10,000Y1+15,000Y2+6,000Y3+8,000Y4+12,000Y5+9,000Y6-800X1-500X2
-600X3-700X4-800X5-600X6-400X7-500X8-400X9-500X10
Constraints:
Constraint 1: each work can work on at most 2 projects
Y1+Y3 +Y5 ≤ 2
Y2+Y4+Y6 ≤ 2
Y2+Y4 ≤ 2
Y1+Y6 ≤ 2
Y1+Y4 ≤ 2
Y3+Y5 ≤ 2
Y2+Y5 ≤ 2
Y1+Y3+Y6 ≤ 2
Y3+Y5 ≤ 2
Y2+Y4+Y6 ≤ 2
Constraint 2: if a project j is undertaken, then all 4 workers required are "used"
4Y1≤ X1+X4+X5+X8
4Y2 ≤ X2+X3+X7+X10
4Y3 ≤ X1+X6+X8+X9
4Y4 ≤ X2+X3+X5+X10
4Y5 ≤ X1+X6+X7+X9
4Y6 ≤ X2+X4+X8+X10
Sign restrictions:
Xi ,Yi are all binary variables