Consider the maximum flow problem network shown below, where the source is node A$,$ the sink is node F$,$

and arc capacities are numbers shown next to these directed arcs.

Page $6$ of $9$

a$)$ Use the augmenting path algorithm described during my lectures and documented on Word document,

$$Chapter $10$ Supplement$-$ Network theory.doc$($posted on the Canvas course page$)$ as well as

described in the assigned course textbook to solve this problem. In solving the problem, please show

me explicitly, how you evaluate each possible augmenting path in the residual network to arrive at the

maximum flow in the network. Redraw the maximum flow problem network with the solved nodes

and arcs, showing respective flows on each arc and ensuring that the conservation property is satisfied

at each node. $(5$ points$)$

b$)$ Formulate and solve a spreadsheet model for this problem using the Excel Solver application tool.

Before submitting, please ensure that the model is working properly and accurately. To earn full points,

the Excel model must have proper comments, wherever appropriate. Note: Please label the Excel

Solver Model and solution as Problem $4$b in a Worksheet in the consolidated Excel file. $(5$ points$)$

Note: Your answers must be full and complete to earn all assigned points for each part of this problem.

Problem $5(10$ points$)$:

You and several friends are about to prepare a lasagna dinner. The tasks to be performed, their immediate

predecessors, and their estimated durations are as follows:

Task Task Description

Tasks that

Must Precede Time

A Buy the mozzarella cheese$*30$ minutes

A

B D

C E

F

$7$

$9$

$7$

$6$

$2$

$4$

$6$

$9$