$1)(40$ 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:

activity

description

immediate predecessors

estimated duration $($min$)$

A

buy the mozzarella cheese

$30$

slice the mozzarella

A

$5$

beat $2$ eggs

$-$

$2$

D

mix eggs and ricotta cheese

$3$

E

cut up onions and mushrooms

$7$

F

cook the tomato sauce

E

$25$

G

boil large quantity of water

$15$

boil the lasagna noodles

G

$10$

I

drain the lasagna noodles

H

$2$

J

assemble all the ingredients

$1,$ F$,$ D$,$ B

$10$

K

preheat the oven

$15$

L

bake the lasagna

I, K

$30$

$(0,30)/$

$30$

$0,30$

Draw a project network representing the preparation of the lasagna.

When can the individual activities start and finish $($at the earliest$)$ if no delays occur?

What is the total time required to make the lasagna if no delays occur? $75$ min When do the individual activities need to start and finish $($at the latest$)$ to meet this completion time?

$$ Which are the critical bottleneck activities where delays must be avoided to prevent delaying the completion of the lasagna? A$,$ B $/$ J$,$L

$$ For the other activities, how much delay can be tolerated without delaying the completion of the lasagna?