Integer model is formulated as below:
Let F1, F2, F3 be the number of full barrels to be given to the three sons respectively.
H1, H2, H3 be the number of full barrels to be given to the three sons respectively.
E1, E2, E3 be the number of full barrels to be given to the three sons respectively.
F1+F2+F3+H1+H2+H3+E1+E2+E3 = 36
s.t.
F1+F2+F3=11
H1+H2+H3=17
E1+E2+E3=8
F1+H1+E1-F2-H2-E2=0
F1+H1+E1-F3-H3-E3=0
F1+.5*H1-F2-.5H2=0
F2+.5*H2-F3-.5H3=0
F1, F2, F3, H1, H2, H3, E1, E2, E3 >= 2
F1, F2, F3, H1, H2, H3, E1, E2, E3 <= 7
Solution using Excel Solver is following:
FORMULAS:
K3 =SUMPRODUCT(B3:J3,$B$14:$J$14) copy to K5:K11
Optimal solution:
Barrels should be distributed as beow:
Full | Half-full | Empty | Total barrels | Total honey | |
Son 1 | 3 | 7 | 2 | 12 | 6.5 |
Son 2 | 3 | 7 | 2 | 12 | 6.5 |
Son 3 | 5 | 3 | 4 | 12 | 6.5 |
Total | 11 | 17 | 8 |
2.With a little thought you should be able to "eyeball" the solution. However the question asks to develop a li...
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