I need help creating/solving a formula

[#686578]

I have so much gold and need to buy two items to craft something, I want to know how much of each I can buy if I need one of each for the synth.

I know price(x)+price(y)=gold will give me the maximum I can buy of both, but two problems, I forgot how to solve this equation (Yeah I know >_>) and also that doesnt take into account I need one of each

I guess the first step is remembering how to solve it, I remember there are three ways to do it, two of them being substitution and I dont remember the name of the other one, but it was like canceling them out but it doesnt really work for complicated equations.

x=(gold-price(y))/(price of x)

Then substitute into the original equation right?

price of x((gold-price(y))/(price of x))+price(y)=gold

And that's solvable... I think?
If that's right, then I just forgot basic principles of math and need help solving because I'm obviously doing something very wrong

100x+50y=500
x=(500-50y)/100

100((500-50y)/100)+50y=500
(50000-5000y)/100)+50y=500
500-50y+50y=500
...wait what 1=1

Wait I think I remembered something

I have to solve to go back and create a formula for y an substitute x into that to solve for x then substitute that into the original problem to find y I think. Man this would've been simpler if I could remember what kind of problem this was to look up examples.

100x+50y=500
x=(500-50y)/100
y=(500-100x)/50

x=(500-50((500-100x)/50))/100
x=(500-500-100x))/100
x=(-100x))/100
x=-x

......wait what I'm so terrible I cant remember shit

After I remember how to solve this fucking thing (or even if I did the formula right) it'll show how much I can buy of each optimally but not take into account how much of each I need so my next step after that will be to manipulate the formula for one of each then that should even be easily manipulated to create a formula if I have a synth that requires different amounts of each item

[BerenTebogo]

10x = 500
x = 50 @ 10 each
50y = 500
y = 10 @ 50 each
price: x/y = 1/5
buy 1 y for every 5 x
5 * 1y = 250
5 * 5x = 250


Not really a straight forward problem but the ratio then plug in numbers usually works.

[Kiarax]

Run. Escape.

[Shiroikage]

RUUUUUNESCAAAAAAPE

[Darkslitter]

10x = 500
x = 50 @ 10 each
50y = 500
y = 10 @ 50 each
price: x/y = 1/5
buy 1 y for every 5 x
5 * 1y = 250
5 * 5x = 250


Not really a straight forward problem but the ratio then plug in numbers usually works.

ur gay

[#686578]

10x = 500
x = 50 @ 10 each
50y = 500
y = 10 @ 50 each
price: x/y = 1/5
buy 1 y for every 5 x
5 * 1y = 250
5 * 5x = 250


Not really a straight forward problem but the ratio then plug in numbers usually works.

This could potentially be useful. I dont know yet if I can make it take into account what numbers of each item I need it to though.

[Klaatu]

Numbers all up in this bitch.

[Klaatu]

btw why are you selling gil?

[#686578]

What

[Dainslaif]

Blah blah math crap.

Well, given the numbers here the answer would be 4 of Y and 3 of X (just by plugging in numbers and seeing which gave the most) but I totally forgot how to solve it legitimately. I think it involves calculus.

Edit: google ftw.
http://tutorial.math.lamar.edu/Class...imization.aspx

[#686578]

Wow I just woke up so a lot of this isnt making sense. I also dont remember this being calculus level but this is definitely the same kind of problem lol

Thanks a lot for finding that, I couldnt remember what kind of equation it was for the life of me or else I would've googled it myself.

Gonna have to read the rest of this later. My calculus class was terrible and never even taught us derivatives so I'm going to have to actually have to learn something new it looks like lol...

[Dainslaif]

To do a derivative, all you do is multiply each chunk of an equation (separated by addition/subtraction) by it's variable's exponent, and then decrease the exponent by one, anything without a variable goes to 0. So, the derivative of 4x^2 would be 8x. Derivative of 8x is 8. Derivative of 8 is 0.

Putting this into practice, the derivative of 5x^2 + 3x + 8 is 10x + 3.

In this case the hardest part is the maximize function. I can't figure out what the formula is for something where x must = y for a unit to be made. Once you get that part it's pretty much cake. The constraint is 100x+50y=500.

[BerenTebogo]

So I took another look at what I wrote last night and I see where I fucked up. You don't need Calculus.

Gonna use retarded numbers for emphasis:
item 1: 1,172g
item 2: 292g
Total gil: 100,000g
Divide the larger number into 100,000. This is your upper bound:
UB: 85.3

1172x + 292y = 100,000
y = 85.3 - x

***EQ1***
1172x +292(85.3 - x) = 100,000
1172x + 24,907.6 - 292x = 100,000
880x = 75,092.4
x = 85.3 (the upper bound)

***EQ2***
1172x + 292(85.3 + x) = 100,000
1172x + 24,907.6 + 292x = 100,000
1464x = 75,092.4
x=51.3

A(85.3) + B(51.3) = 136.6
136.6 / 2 = 68.3

68.3 * 1172 = 80,047'6
68.3 * 292 = 19,943.6
= 99,991.2 gil

Round it down to 68. You can buy 68 of each at 1,172 for A and 292 for B.

I dunno why that took my brain so long to churn out.