### Solving the Motorcycle Madness Upgrade Problem

9 Comments Published May 28th, 2009 in Entertainment, tips&tricks#### Problem 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.

#### 9 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
- 3 Trackback on Sep 28th, 2021 at 5:49 pm
- 4 Trackback on Oct 7th, 2021 at 2:50 pm

Ha! Nice use of mathematics ðŸ™‚

naturally like your website but you have to test the spelling on several of your posts.

Many of them are rife with spelling problems and I to find it

very bothersome to tell the truth on the other hand I will certainly come again again.

What’s up, the whole thing is going nicely here

and ofcourse every one is sharing facts, that’s really good, keep up writing.

Very nice blog post. I definitely appreciate this website. Keep writing!

Hmm is anyone else experiencing problems with the images on this blog loading?

I’m trying to determine if its a problem on my end or if it’s the blog.

Any feedback would be greatly appreciated.