Question: Please use LINGO to solve part c . The answer for b is below with the question. Answer for b: A furniture store at location

Please use LINGO to solve part c. The answer for b is below with the question.

Answer for b:

A furniture store at location 0 has deliveries to make to customers at locations 1,2,3, and 4. The time in minutes that it would take a truck to travel from one location to another is given in the following table. Because of one-way streets and places where no left-turn are allowed, or are difficult to make, the table is not symmetric. The objective is to minimize the total travel time. (a) Give the algebraic model of this situation, omitting the sub-tour constraints. (b) Use LINGO or the Exeel Solver to solve this (partial) model. Show that this solution is not a tour, and state the two sub-tours. (c) Give a constraint that would, if added to the formulation of (b), prevent this specific situation from arising. Re-solve the computer model, and state whether or not this new solution is a tour. Let Xij be the binary integer such that Xij=1 when the arc from node-i to node-j is selected in the optimal path and Xij=0 otherwise. Minimize Z= total distance = 2501+3702+4503+3304+2510+1612+3213+1814+2920+1721+2823+2224+4530+3631+3032+1534+3140+2341+2842+1743 Subject to, Only one exit from node-i X01+X02+X03+X04=1(exitfromnode0)X10+X12+X13+X14=1(exitfromnode1)X20+X21+X23+X24=1(exitfromnode2)X30+X31+X32+X34=1(exitfromnode3)X40+X41+X42+X43=1(exitfromnode4) Only one entry to node-j X10+X20+X30+X40=1 (entry to node 0) X01+X21+X31+X41=1 (entry to node 1 ) X02+X12+X32+X42=1 (entry to node 2 ) X03+X13+X23+X43=1 (entry to node 3 ) X04+X14+X24+X34=1 (entry to node 4 ) Solution: Global optimal solution found. Objective value: 102.0000 Infeasibilities: 0.000000 Total solver iterations: 7 Elapsed runtime seconds: 0.08 Model Class: LP Total variables: 20 Nonlinear variables: 0 Integer variables: 0 Total constraints: 11 Nonlinear constraints: 0 Total nonzeros: 60 Nonlinear nonzeros: 0 Variable Value Reduced Cost X01 1.0000000.000000 X02 0.0000009.000000 X03 0.00000020.00000 X04 0.0000008.000000 X10 0.0000000.000000 X12 1.0000000.000000 X13 0.00000019.00000 X14 0.0000005.000000 X20 1.0000000.000000 210.0000000.000000 230.00000011.00000 X24 0.0000005.000000 300.00000018.00000 310.00000021.00000 X32 0.00000012.00000 X341.0000000.000000 400.0000002.000000 X41 0.0000006.000000 X42 0.0000008.000000 X43 1.000000 0.000000

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