Project Proposal Early Submission Bonus
=======================================

In order to encourage students to commence work on the project as early
as possible during the term (in order to save themselves much pain
and suffering towards the end of the term), I have instituted a bonus
mark system for the project proposal.  Also, in order to reduce the
likelihood that a large number of students submit their proposal at
the same time in order to be able to receive a bonus, the bonus is
not associated with one particular deadline date.  Instead, the bonus
starts at a maximum initial value and then slowly decays over time
until it reaches zero.

The bonus is a simple multiplicative bonus.  In other words, the bonus
is applied in the following manner:

Let G denote the grade on the project proposal without considering the bonus.
Let G' denote the grade on the project proposal after any applicable bonus
is applied.
Let F denote the (multiplicative) bonus factor.
Then, G' is calculated from G as follows:

  G' = F G (*)

The precise manner in which F is determined will be explained in a
later section.

Eligibility Requirements
------------------------

As part of the evaluation process for the project proposal, the instructor
makes a decision as to whether the proposed project is acceptable.
This decision can have one of several possible outcomes:

  - Unconditionally accepted
  - Conditionally accepted
  - No decision
  - Rejected

In order to be eligible for the early submission bonus, a project
proposal must receive a decision of either "Unconditionally accepted"
or "Conditionally accepted".  This constraint is intended to prevent
students from deliberately submitting low-quality work early with the
sole objective of maximizing the amount of bonus to be received.

Bonus Calculation
-----------------

Day of Final Submission Deadline:
Wed Jul 3 (as stated on course website)
[NOTE: This date should match the one on the course website!]
After this deadline, the project proposal is deemed late.
(According to the project handout a grade of zero will be awarded in
this case.)

Starting Day of Early-Bonus Decay Period:
Wed May 29 (approximately 5 weeks before final submission deadline)

Ending Day of Early-Bonus Decay Period:
Wed Jun 26 (approximately 1 week before final submission deadline)

Let S denote the day (stated above) on which the early bonus starts to
decay from its initial maximum value.
Let E denote the day (stated above) on which the early bonus decay period ends.
Let D denote the day on which the project proposal is submitted.
The quantities S, E, and D are integers denoting the calendar day offset
from the first day of the year (i.e., S, E, and D are integers in the
range 0 to 364).
Let D' denote the day that the project proposal is submitted relative to S
(i.e., D' = D - S).
The multiplicative bonus factor F (from (*) earlier) is calculated as follows:

  if D' < 0 (i.e., the proposal is submitted prior to the start of the
  early-bonus decay period):
  F = 1 + 0.10 = 1.10 (i.e., full bonus)

  if D' >= 0 and D' < E - S (i.e., the proposal is submitted during the
  early-bonus decay period):
  F = 1 + 0.10 [(E - S - D') / (E - S)] (i.e., partial bonus)

  if D' >= E - S (i.e., the proposal is submitted at, or after, the end
  of the early-bonus decay period):
  F = 1 (i.e., no bonus)

For example, if the bonus decay period is 28 days (i.e., E - S = 28)
and the proposal is submitted on day 14 of the early-bonus decay period
(i.e., D' = 14), we have

  F = 1 + 0.10 [(28 - 14) / 28] = 1 + 0.10 (0.5) = 1.05

Note that the above formula results in a bonus factor that decays linearly
from a maximum of 1.10 (i.e., 10% bonus) to 1 (i.e., no bonus).