Problem $1$: Transportation Network Model $(30)$

Given: The highway network shown in the diagram below represents possible routes for vehicles

traveling from node $1$ to $7.$ Node $7$ is a toll plaza for a critical bridge crossing.

All possible route capacities $($vehicles$/$hr$)$ are given in the shaded cells of the matrix table below.

Route Capacity Matrix $($ veh$/$hr$)$

Find: The maximum flow of traffic $($veh$./$hr$.)$ possible traveling through the highway network

from node $1$ to $7$ and entering the bridge toll plaza.

Formulate the above problem as a linear program. Clearly define the decision variables,

objective function, and constraints. General mathematical expressions are acceptable.

$(15)$

a$.$ Decision Variables:

b$.$ Objective Function:

c$.$ Constraints:

Solve the problem using Excel Solver. You must provide screen shots of the solver

model and solution in Excel to receive credit. $(15)$

a$.$ Maximum flow of traffic entering toll plaza at node $7$ is

veh$/$hr$.$