$1-$ Given the following network:

a$)$ Find the earliest time the project will be completed.

b$)$ Find the critical path..

c$)$ If activity I is delayed by $5$ days, find the completion time of the entire project.

Activity t G

A $10$

B $8$ A

C $13$ E H

D $8$ C

E $7$ D

F $12$

G $13$ B F I

H $5$

I $10$

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$2$ A food processor company uses approximately $10$ glass jars a day for its fruit juice

product. Weekly holding cost is $$0\mathrm{.}20$ per jar, and ordering cost is $$40$ per order.

a$.$ Find optimal order quantity?

b$.$ What penalty is the company incurring if they currently order Q$=300?$

c$.$ If ROP$=40,$ find LT$..$

d$.$ Find number of orders per year.

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$3-$ ABC textile mills produces a special cloth. The demand for this cloth is $10$ yards per day. The production

setup $($ordering$)$ cost is $$100$ per order and holding cost is $$\mathrm{.}20$ per week. If production rate is $600$ yards per

month, find;

a$)$ Compute the optimal order quantity

b$)$ Compute the production run time.

c$)$ Find maximum inventory level.

d$)$ Find the total cost

e$)$ If SS$=25,$ find TC$.$

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$4-$ Given the following product structure $($BOM$)$ and inventory status. Determine the quantity and timing of each

component that must be produced. Planned order for component A is $50$ units in period $10.$

Item OH$(1)$

A $($LT$=1)$

A $0$

B $30$

D$($LT$=4)$ F$($LT$=3)$ C$($LT$=2)$ C $50$

$3$ units $2$ units $4$ units D $40$

E $100$

F $50$

B$($LT$=3)$ F$($LT$=3)$ B$($LT$=3)$ E$($LT$=5)$ D$($LT$=4)$

$4$ units $1$ unit $1$ unit $3$ unit $2$ units