5) (20 points) A network is given with the link number e=1,2,....E. The demand number is d=1.2.1.D. The demand is denoted as ha. The candidate path number for each demand d is p=12ww.Pd. The link-path relationship Oedp is given for every end.p. Dedp=1 means link e belongs to path p for demand d. The unit transmission cost for each flow Xdp is Sdp. Please write the optimization formulation. a) use flow demand (Xdp) and link capacity ye as variables; b) the constraints needs to be satisfied. c) The total transmission cost is to be minimized. 6) (15 Points) A network is given with the link number e=lizow.E. The link capacity is ce The demand number is d=12m..D. The candidate path number for each demand d is p=www.Pd. The link-path relationship Dedp is given for every ead.p. Proportional fairness method is used. Please write the optimization formulation including both objective function and constraints. a) use Xa as the total demand volume variable allocated to demand d, use Xdp as the flow demand variables. b) Revenue objective: maximizing the sum of (natural) logarithms of the volumes assigned to demands. c) constraints(capacity and demand constraints) are satisfied. 5) (20 points) A network is given with the link number e=1,2,....E. The demand number is d=1.2.1.D. The demand is denoted as ha. The candidate path number for each demand d is p=12ww.Pd. The link-path relationship Oedp is given for every end.p. Dedp=1 means link e belongs to path p for demand d. The unit transmission cost for each flow Xdp is Sdp. Please write the optimization formulation. a) use flow demand (Xdp) and link capacity ye as variables; b) the constraints needs to be satisfied. c) The total transmission cost is to be minimized. 6) (15 Points) A network is given with the link number e=lizow.E. The link capacity is ce The demand number is d=12m..D. The candidate path number for each demand d is p=www.Pd. The link-path relationship Dedp is given for every ead.p. Proportional fairness method is used. Please write the optimization formulation including both objective function and constraints. a) use Xa as the total demand volume variable allocated to demand d, use Xdp as the flow demand variables. b) Revenue objective: maximizing the sum of (natural) logarithms of the volumes assigned to demands. c) constraints(capacity and demand constraints) are satisfied