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)	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

Overall Hint: For any question that involves crashing, make sure that you stick to the definitions of normal time/cost and crash time/cost of each activity to figure them out. Here they are again:

Normal time for an activity: The duration of the activity if no expedition of any sort happens for that activity.

Normal cost for an activity: The cost of carrying out the activity with the duration of "normal time".

Crash time for an activity: The duration of the activity if the maximum amount of expedition happens for that activity.

Crash cost for an activity: The cost of carrying out the activity with the duration of "crash time".

Remember that (normal/crash) cost can be represented either as the total cost of the activity or the additional cost of an activity compared to some fixed benchmark or sunk cost. Please make sure you are clear as to how you are accounting for cost and whether or not you are assuming any sunk cost in your calculations.

Question 1

What is the minimum project completion time?

Question 2

How many activities should be completed 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)

Group of answer choices

XD XG +18

XG XD +18

XD XG +26

XG XD +26

The company has planned to launch an advertising campaign in conjunction with its mass introduction. Therefore, the product should be available for mass introduction (i.e. project completed) on or before the start date of the advertising campaign. The advertisement announces that the product is available from a date which coincides with the 65^th day after the start of the project. The company realizes that the base cost for each of the activities needs to be paid no matter what and can be considered as sunk cost, but is now considering the possibility of spending more (and the least possible) to expedite the duration of activities E, D, and/or G either fully or partially so that the project can be carried out on time:

The duration of activity D can be shortened by 5 days at an additional cost of $2000.

The duration of activity E can be shortened by 3 days at an additional cost of $5000.

The duration of activity G can be shortened by 5 days at an additional cost of $3000.

Question 8

By how many days the duration of activity G is best to be shortened?

Question 9

In doing the above expedition, how much additional cost will be incurred?

The company finally decides to only expedite activity D by 1 day which incurs an additional cost of $400 (=$2000 of full expedition cost /5) when this activity is 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 (i.e., $40).

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

Question 10

Continuing this progress, what is the earliest time the project can be expected to finish? (enter in unit of days and counted from the beginning of the project)

Question 11

Eli Orchid is trying to figure how to expedite the project at this point, after seeing the progress until day 25. It can still expedite the same activities D, E, and G with the cost structure stated above. Since activity D is expedited a little bit so far, it is still possible to expedite it "further" 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 day 65, given the current progress, how much more would it have to pay from this point on (in addition to what is already spent for activity D, i.e. 10% of $400)?

Hint: First, 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.