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 Excel 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.

From To 0. 1 2. 3. 4 0 22 34 25 0 16 32 18 0 28 45 36 30 42 30 29 17 0 28 22 3 15 28 20 25 14 0. 21100 4