The Reliable Construction Company has just made the winning bid of $$5\mathrm{.}4$ million to construct

a new plant for a major manufacturer. The manufacturer needs the plant to go into operation

within $40$ weeks. The following table shows the activities that this project involves. The total cost

of the activities is about $$4\mathrm{.}55$ million.

Activity Activity description Immediate

predecessors

Estimated duration

$($weeks$)$

A Excavate $\_2$

B Lay the foundation A $4$

C Put up the rough wall B $10$

D Put up the roof C $6$

E Install the exterior

plumbing

C $4$

F Install the interior

plumbing

E $5$

G Put up the exterior

siding

D $7$

H Do the exterior

painting

E$,$ G $9$

I Do the electrical work C $7$

J Put up the wallboard F$,$ I $8$

K Install the flooring J $4$

L Do the interior

painting

J $5$

M Install the exterior

fixtures

H $2$

N Install the interior

fixtures

K$,$ L $6$

a$.$ Draw an activity$-$on$-$node network that represents this problem

b$.$ Find the critical path$($s$)$ and the project completion time. Estimate the slack time on each of

the non$-$critical activities

c$.$ Determine which task to crash and by how much time and cost in order to reduce the project

completion time to $40$ weeks. Table below has the normal duration of each activity, the minimum

duration if the activity is fully crashed $($i$.$e$.$ column labeled as crash$),$ the normal cost of the

activity, its cost if crashed. Use the table information as needed to answer the questions below.

$2$

Time Cost $($Thousands of $$)$

Normal

duration

$($weeks$)$

Crash

$($weeks$)$

Normal Crash

A $21180280$

B $42320420$

C $107620860$

D $64260340$

E $43410570$

F $53180260$

G $749001020$

H $96200380$

I $75210270$

J $86430490$

K $43160200$

L $53250350$

M $21100200$

N $63330510$

$1.$ What is the least expensive way of crashing some of the activities to reduce the

project completion to $40$ weeks? Write in chronological order which activities to

crash and for how many weeks?

$2.$ What is the total cost of crashing the activities you selected in $1?$

$3.$ What is$/$are the new critical path$($s$)?$

$4.$ What is the total project cost if crashing the activities you suggested