$1-$ Given the following network:

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

b$)$ Find the critical nath.

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

$\backslash$table$[[$Activity t$,],[$A$,8],[$B$,6],[$C$,11],[$D$,6],[$E$,7],[$F$,11],[$G$,12],[$H$,10],[$I$,10]]$

$2-$ A food processor company uses approximately $10$ glass jars a week for its fruit juice product. Monthly holding cost is $$0\mathrm{.}10$ per jar, and ordering cost is $$40$ per order.

a$.$ Find optimal order quantity?

b$.$ What penalty is the company incurring if they currently order $Q=200?$

c$.$ If ROP$=20,$ find LT$?$

d$.$ Find time between orders.

$3-$ ABC textile mills produces a special cloth. The demand for this cloth is $20$ yards per week. The production setup $($ordering$)$ cost is $$80$ per order and holding cost is $$\mathrm{.}50$ per month. If production rate is $200$ 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 $SS=15,$ find $TC.$

$4-$ 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 $10.$