Problem $2(25)$

Given: A highway network with route capacities $($vehicles $\frac{?}{hr})$ is illustrated in the figure below.

$($All arcs are two$-$way, Capacity shown is veh$/$hr$)$

Find: Maximum traffic flow $($veh$./$hr$.)$ through the network for vehicles entering node $1$ and

exiting node $6.$

Formulate the following elements of a linear program using general mathematical expressions

for:

a$.$ Decision variables $(5),$

b$.$ Objective function $(5),$ and

CIVE $5810$ Engineering Systems Analysis

Name:

HW$3$: Network Models $($Max pts $=75)$

Page $2$ of $2$

c$.$ constraints $(5).$

Formulate the problem and solve using MS Excel Solver. Provide screen shots of your model

including decision variables, objective function, constraints, and solution. $(10)$Problem $1$: $(25)$ Problem $2(25)$ Given: A highway network with route capacities $($vehicles $/$hr $)$ is illustrated in the figure below. $($All arcs are two$-$way, Capacity shown is veh$/$hr$)$ Find: Maximum traffic flow $($veh$./$hr$.)$ through the network for vehicles entering node $1$ and exiting node $6.$ Formulate the following elements of a linear program using general mathematical expressions for: a$.$ Decision variables $(5),$ b$.$ Objective function $(5),$ and CIVE $5810$ Engineering Systems Analysis Name: HW$3$: Network Models $($Max pts $=75)$ Page $2$ of $2$ c$.$ constraints $(5).$ Formulate the problem and solve using MS Excel Solver. Provide screen shots of your model including decision variables, objective function, constraints, and solution. $(10)$ Problem $3(25)$ Given: A highway network with each route length $($miles$)$ is illustrated in the figure below. $($All arcs are two$-$way, distance shown is miles$)$ Find: The shortest path $($miles$)$ through the network for vehicles entering node $1$ and exiting node $6.$ Formulate the following elements of a linear program using general mathematical expressions for: a$.$ Decision variables $(5),$ b$.$ Objective function $(5),$ and c$.$ constraints $(5).$ Formulate the problem and solve using MS Excel Solver. Provide screen shots of your model including decision variables, objective function, constraints, and solution. $(10)$ Given: Massachusetts Block Company $($MBC$)$ has orders for $80$ tons of concrete masonry blocks at three locations as follows: Lowell $=25$ tons, Salem $=45$ tons, and Worchester $=10$ tons. MBC has two plants; Plant $2$ can produce up to $50$ tons per week while Plant $1$ can only produce a maximum of $40$ tons per week. The deliveries must be shipped through two warehouses before reaching their final destination. Delivery costs per ton between each location and capacity at each location are provided below: Find: a$)$ Formulate the LP problem with Network Diagram and mathematical expression for decision variables, objective function, and constraints $(10)$ b$)$ Solve for the minimum cost shipping plan using Excel Solver. Illustrate the optimal shipping plan in a network diagram. $(15)$