A problem formulation is given below:

MAX FLOW( 6, 1) SUBJECT TO FLOW( 1, 2) <= 2 FLOW( 1, 3) <= 3 FLOW( 2, 3) <= 3 FLOW( 2, 4) <= 4 FLOW( 3, 5) <= 2 FLOW( 4, 5) <= 1 FLOW( 4, 6) <= 2 FLOW( 5, 6) <= 3 FLOW( 6, 1) <= 1000 -FLOW( 1, 2) - FLOW( 1, 3) + FLOW( 6, 1) = 0 FLOW( 1, 2) - FLOW( 2, 3) - FLOW( 2, 4) = 0 FLOW( 1, 3) + FLOW( 2, 3) - FLOW( 3, 5) = 0 FLOW( 2, 4) - FLOW( 4, 5) - FLOW( 4, 6) = 0 FLOW( 3, 5) + FLOW( 4, 5) - FLOW( 5, 6) = 0 FLOW( 4, 6) + FLOW( 5, 6) - FLOW( 6, 1) = 0

Based on this formulation, an incorrect LINGO Model is given below:

MODEL: SETS: NODES/1..5/; ARCS(NODES,NODES)/1,2 1,3 2,3 2,4 3,5 5,6 6,1/:CAP; ENDSETS MAX=FLOW(6,1); @SUM(ARCS(I,J):FLOW(I,J)<=CAP(I,J)); @FOR(NODES(I):@FOR(ARCS(J,I):FLOW(J,I))=@SUM(ARCS(I,J):FLOW(I,J))); DATA: CAP=2,3,3,4,2,1,2,3,1000; ENDDATA END

Which parts are wrong in this LINGO model? Please circle the parts that are wrong and correct them (rewrite the correct model) and explain your corrections in details to get credit