↫↫↫ Scientia Est Potentia ↬↬↬


Proportional function of Contraband

BY M. G. EQUINOX AND A. M. S. PANDA
REVIEWED AND CONFIRMED BY dr. A. P, PhD in Maths


1.Complexity
In game we meet 2 different types of contraband. One is Money printer, which costs $1,000 to buy ($2,000 for 2) and produces $250 ($500 for 2) each cycle of 5 minutes.
Second contraband is Drug lab, which costs $750 to buy ($3,750 for 5) and produces $140 ($700 for 5) each cycle of 5 minutes. Total cost for all 7 contraband units is $5,750.




2. Periodical problem
Money from contraband units can only be collected every 5 minutes, that's why we have to integrate all time intervals
between cycles, thus giving us natural variables on cartesian abscissa axis. Integration is done between each cycle
and cycle before it.





3. Cartesian solution
We can define proportionality of time and money from contraband units with proportional function g(T)=k*|T|+n, whereas
T is number of 5 minute cycles, k stands for total money collected from all contraband units in one cycle and n starting
money, in our case negative integer.







Notes: The X axis is number of cycles and not number of minutes
This plot is displaying function of money produced from contraband objects without other incomes or outcomes.
From plot we can read that after 5 cycles (25 minutes) we get money for contraband units refunded (plus additional $250)
For cycle variable function needs absolute value since time can not have negative value


4. Leibniz fundamental theorem of calculus
Each function can be derived to obtain its tangent coefficient, which tells us how fast is function ascending or descending
proportional to X axis. Derivatives can be calculated using Leibniz way using limits or Euler's form.



in our case





Note: Second derivative since we already integrated time into cycles



At the end we came to results that tangent coefficient is constant, which is expected.

5. Realistic approach
To make our proportional function more realistic, we need to add more variables, including sallary, rent and items equipped
by player. Some of those still change depending of current X axis cycle, some of which are only applied at start.



Kr = rent per cycle (5 minutes)
Ks = sallary per cycle (5 minutes)

Na = price of ammunition used on start (insert 0 if none)
Nk = price of kevlar used on start (1500 if used, otherwise insert 0)
Nw = price of weapon used on start (insert 0 if none)    *insert 0 if you holster it and not loose it via death for example

Special thanks to:
A. P.
[FL:RP] Trixie
[FL:RP] LordOfMemory
SoulRipper
Fearless Community © 2008-2017
and you for reading this publication

Signed:
M. G. Equinox
A. M. S. Panda


↫↫↫ Scientia Est Potentia ↬↬↬