Please solve only questions

9 and 10

Instructions

If you remember from mini-project 1, Eli Orchid was introducing its new product Orchid Relief to the market. The company has decided on the following strategy to mass introduce the product to California:

First introduce the product to Los Angeles, get a better idea of demand volume and customer taste in packaging of the product, and then finalize the package design and mass produce the product for distribution to California. The company created the following breakdown of tasks to be completed.

Activity code	Activity	Immediate predecessor(s)	Average duration (days)
A	Produce and distribute a test batch of Orchid Relief for LA	None	12
B	Advertise in LA	None	12
C	Gather preliminary sales data after the 1st week of sales in LA	A, B	9
D	Produce a few tons of Orchid Relief for mass introduction that would definitely be sold based on preliminary data	C	26
E	Gather final sales data after 3 weeks of sales in LA	C,B	23
F	Advertise in whole California	C	16
G	Produce the remaining tons of Orchid Relief for mass introduction based on total sales in LA	E,D	18
H	Package Orchid Relief produced based on sales data obtained	E,G	7

Question 1:

What is the minimum project completion time?

Question 2:

How many activities should be completed one right after the other as soon as possible and without interruption?

Question 3:

How many critical paths are there in this project?

Question 4:

In order to plan for mass production as soon as possible, Eli Orchid would like to obtain data from market research (activity E) as soon as possible. What is the earliest time the company would have this data fully available and can use it?

Question 5:

If activity A is delayed by 5 days, how many days of delay would the project completion time experience?

Question 6:

If activity E is delayed by 5 days, how many days of delay would the project completion time experience?

Question 7:

Which of the following constraints would describe the relation of activities G and D in a linear programming formulation for finding the earliest start times of activities? (Let XD and XG be the earliest start times of activities D and G respectively)

Select one:

XG XD +26

XD XG +26

XG XD +18

XD XG +18

(Part 2):

In the analysis of the following 2 questions, assume that no uncertainty exists in durations of any of the activities.

The company finally decides to proceed with running the project with only expediting activity D by 1 day only which would additionally cost $400 (=$2000 of full expedition cost /5) when fully completed.

After 25 days passes from the start of the project, the following progress is made through the project. Note that the progress of 10% in activity D is done according to the plan of its 1-day expedition (i.e. with respect to a duration of 25 days) which, by the progress so far in the project, has already incurred 10% of the projected total cost as well.

Activity	A	B	C	D	E	F	G	H
Progress on day 25	100%	100%	100%	10%	20%	0%	0%	0%

Question 9:

Continuing this progress, which day (counted from the beginning of the project) can the project be planned to be finished at best?

Question 10:

Eli Orchid is trying to figure how to expedite the project at this point, after seeing the progress until day 25. The activities it can expedite are the same activities D, E, and G. Since activity D is expedited a little bit so far, it is still possible to expedite it "further" than the current amount for the remainder of this activity (but we cannot slow it down to no expedition at this point). Assume that the remaining duration and cost (both regular and expedited cases) are proportional to the remaining percentage progress of each activity. If the company still likes to finish the project by the same target of day 65, given the current progress, how much more would it have to pay for expediting activities from this point on (in addition to what is already spent for activity D by day 25, i.e. 10% of $400)?

Hint: in the first step, assume it is time 0, and lay down normal/crash time & cost (note that activity D has already been decided to be expedited by 1 day meaning a normal cost of $400, but it is allowed to be expedited more). Then revise them according to the fact that 25 days has passed.