Solving the Motorcycle Madness Upgrade Problem
7 Comments Published May 28th, 2009 in Entertainment, tips&tricksProblem definition:
Given your balance, pick a subset of upgrades such that summation of Power, Traction and Aerodynamics are maximized and summation of costs doesn’t exceed balance. Problem can be found on this page: http://apps.facebook.com/motorcycle_madness/upgrade.php
Solution:
We will use linear programming method. Let’s use an example here. For the initial problem:
Balance: $73,845
Upgrades available:
Suspension
Traction: +30
Aerodynamics: +50
Cost: $30,000
Sport Stabilizer
Traction: +50
Cost: $25,000
Transmissions
Power: +20
Traction: +30
Cost: $35,000
Jet Kit
Power: +50
Cost: $40,000
Nitrous Kit
Power: +100
Cost: $80,000
Tires
Traction: +30
Cost: $18,000
Throttle Body
Power: +25
Cost: $17,500
Brakes
Traction: +20
Cost: $12,000
Stealth Radiator Cover
Aerodynamics: +50
Cost: $10,000
Exhaust
Power: +30
Cost: $20,000
Air Filters
Power: +20
Cost: $15,000
Steps:
- Assign a variable for each upgrade and find cumulative gain for each. Cumulative gain is addition of gains in each category (Power, Traction and Aerodynamics).
(gain x1000)variable upgrade gain a Suspension 80 b Sport Stabilizer 50 c Transmissions 50 d Jet Kit 50 e Nitrous Kit 100 f Tires 30 g Throttle Body 25 h Brakes 20 i Stealth Radiator Cover 50 j Exhaust 30 k Air Filters 20 - Write down objective function as summation of each upgrade multiplied by its gain.
p = 80a+50b+50c+50d+100e+30f+25g+20h+50i+30j+20k - Write down balance constraint as summation of each upgrade multiplied by its cost.
30a+25b+35c+40d+80e+18f+17.5g+12h+10i+20j+15k <= 73 - Write down supply constraints. Only one upgrade is available for each of them.
a <= 1, b <= 1, c <= 1, d <= 1, e <= 1, f <= 1, g <= 1, h <= 1, i <= 1, j <= 1, k <= 1 - Go to an online linear programming solver site, ex. http://www.zweigmedia.com/RealWorld/simplex.html
- Type your problem into problem box.
Maximize p = 80a+50b+50c+50d+100e+30f+25g+20h+50i+30j+20k subject to
30a+25b+35c+40d+80e+18f+17.5g+12h+10i+20j+15k <= 73
a <= 1
b <= 1
c <= 1
d <= 1
e <= 1
f <= 1
g <= 1
h <= 1
i <= 1
j <= 1
k <= 1 - Click “Solve”. Optimal solution appears below.
p = 193.333; a = 1, b = 1, c = 0, d = 0, e = 0, f = 0.444444, g = 0, h = 0, i = 1, j = 0, k = 0
That is, you should buy upgrades a (Suspension),b (Sport Stabilizer) and i (Stealth Radiator Cover).
f (0.444444) is smaller than 1, so there is not enough balance left after buying a,b and i and it will not be bought.
That’s all. Good luck.
7 Comments to “Solving the Motorcycle Madness Upgrade Problem”
- 1 Trackback on Dec 23rd, 2018 at 12:20 pm
- 2 Trackback on Jan 6th, 2021 at 4:01 am
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