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1. When an accounting firm audits a corporation, the first phase of the audit involves obtaining " knowledge of the business" . This phase of the audit requires the activities in the following table:

Activity	Description	Immediate predecessors	Duration(Days)
A	Determining terms of engagement	-------	4
B	Appraisal of auditability risk and materiality	A	6
C	Identification of types of transactions and possible errors	A	14
D	Systems description	C	8
E	Verification of systems description	D	4
F	Evaluation of internal controls	B,E	8
G	Design of audit approach	F	9

(A) Draw the project network using an AOA( Activity on arc) representation.

(B) Use POM-QM or Excel Add- In to determine the critical path for the network.

(C) Use LINGO and a linear programming model to find the critical path.

(D) Assume that the project must be completed in 30 days. The duration of each activity can be reduced by incurring the costs shown in a table given below. Formulate a Linear programming model and use LINGO and the model to minimize the cost of meeting the project deadline.

Activity	Cost per Day of Reducing Duration of Activity($)	Maximum possible reduction in duration activity( Days)
A	110	3
B	90	4
C	70	5
D	80	2
E	40	2
F	35	4
G	60	4

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