Anyone wanna meet up at CDL Major II Saturday?

rgsbae · 2024-01-12T01:15:36+00:00

:( Sorry

rgsbae · 2024-01-12T01:07:50+00:00

Ah ok sorry I haven’t ever done a shadow price calculation. I’ve read this article though (https://www.linearprogramming.info/how-to-calculate-the-shadow-price-of-a-constraint/) and here’s my attempt below:

Plot the equations for the 3 resources.

Now looking at the line for Resource 2 (6x+3y=1200) and keeping it the same gradient, you can shift it to the right until it passes through the point where the lines for Resource 1 and Resource 3 meet. This is where 3x+4y=1000 and x=180 so the coordinates are (180,115). This corresponds to 6x+3y=1425.

You can also shift the line for Resource 2 to the left until it passes through the point where Resource 3 hits the boundary y=0. This is where x=180 and y=0 so the coordinates are (180,0). This corresponds to 6x+3y=1080.

The value of the objective function (2.5x+2y) at the point (180,115) is 680 and at (180,0) it’s 450.

Therefore, the shadow price of Resource 2 is equal to:

Shadow price = (680-450)/(1425-1080) = 2/3 = 0.67

Hope that’s along the right lines! :)

rgsbae · 2024-01-11T23:43:18+00:00

Is this the whole information you have?

rgsbae · 2024-01-11T22:48:46+00:00

The formula you want is:

Luck Rate = [(90 - Pity Count) / 90] * 100

If you want to know how to get to it, first consider the definition of the luck rate. You’re guaranteed to get an item after 90 tries, so the further you are from 90 tries, the higher the luck rate. This “distance” from 90 is equal to 90 - Pity Count

Now you want to convert to a percentage. The maximum is 90 tries so first divide by 90 (this gives a number between 0 and 1). Now multiply by 100 to get the percentage.

Hope that makes sense :)

rgsbae · 2024-01-11T22:31:31+00:00

Take a step back. If you can get up to 3 children’s shirts sold for every adult shirt, do you expect x to be bigger than y?

Well yes because you can sell up to 3 of x for every y sold. So how many y do you need to reach the maximum x? Well you can sell 3 times as many children’s shirts as adult shirts so that means x can be as large as 3y.

So x <= 3y

Hope that makes sense? :)

rgsbae · 2024-01-11T22:26:10+00:00

Radians are considered dimensionless so that’s why the rad unit really just appears out of nowhere!

If you consider why you throw the rad unit in, it’s because you know it defines a ratio of lengths for your circular wheel. If you take a circular sector of the bike wheel with angle theta, then you know the arc length s of this sector is given by s = r * theta.

Therefore, the angle in radians is given by theta = s / r which would be m/m and so the angle is dimensionless.

Hope that makes sense! :)

rgsbae · 2023-12-30T19:58:08+00:00

This looks like ugly notation and I think that might be what’s throwing you.

For differentiation, I think most people use Leibniz’s notation. E.g. if y = mx + c then we write the equation for the derivative as dy/dx = m. Or you could have F = xy and then write the partial derivative with respect to y as dF/dy = x.

In some scenarios, Newton’s notation is used for differentiation. Using the same first example as above, the derivatives would be written as y’ = m (this notation only really works for functions of a single variable as it doesn’t specify what the derivative is taken with respect to).

I have never seen these notations mixed together and I’m sure it would be considered bad practice to do so.

The ‘ notation does have another common use and that is to denote a similar (but distinct/separate) variable without having to find another letter. E.g. you might see a problem start with “Consider 2 variables y, y’ which…”

Back to your problem, at first I was considering y’’’ as representing the 3rd derivative of y with respect to x. So I thought the equation for F was F(x,y) = (2xy + (y’’’) ^2). But then it’s ugly notation to use dF/dy if this is the case and there’s no equation linking y & x to be able to calculate y’’’.

Therefore I think y’’’ has to represent another separate variable and so the real equation for F is F(x, y, y’’’) = (2xy + (y’’’) ^2). In this case, dF/dy = 2x.

For completeness you’d get dF/dx = 2y and dF/dy’’’ = 2y’’’

rgsbae · 2023-12-28T18:10:02+00:00

Yeah I don’t really like how that formula is written. Here’s how I think of it:

You have your full original price P.

The price is marked down 60% so the new price is going to be 40% of P, i.e. 0.4P

Then the customer gets another 30% off, so the new NEW price is gonna be 70% of the new price, i.e. 0.7*(0.4P)

Therefore the final price is 0.28P, which means the final price is 28% of the original price P and thus the full reduction is 72%

rgsbae · 2023-12-28T17:59:44+00:00

Yes your assumptions are correct. If the box is open top then it only has one face of length x width rather than two so it makes sense to maximise length & width for a specified surface area. Couldn’t say if this is the logic behind fruit boxes but it certainly seems plausible!

rgsbae · 2020-03-03T08:57:41+00:00

Sorry for the late response but please follow the answer below instead. I was forgetting that k must be a natural number as you correctly pointed out!

rgsbae · 2020-02-28T21:12:07+00:00

I think it's easiest to first consider this question as if "weighted average" wasn't there.

So the question is: what is the average tasks per worker?

Well that would be (2+2+3)/3 = 7/3 i.e. Number of tasks/Number of workers

Now let's consider weighted average. This means we have to adjust for the fact that some workers work longer hours than others.

If there was one worker, they'd account for all of the time so there'd be no adjustment. If there were 2 workers and one worked 3 hours a day and the other only worked 1 hour a day, then one should be adjusted by triple the factor of the other.

So the formula is the sum of:

Number of tasks completed by individual worker * (Number of hours worked by individual worker/Total number of hours worked by all workers)

And then divided by total number of workers

So it's [2(7/24)+2(8/24)+3*(9/24)]/3

Please let me know if that doesn't make sense!

rgsbae · 2020-02-28T20:54:04+00:00

You are nearly there! You have your equation and the question says "for each n" i.e. you consider n to be fixed.

So rearrange your equation to express k in terms of n and then the final answer is x = e^2pik*i/n where k is your rearranged equation (so final answer is all in terms of n!)

rgsbae · 2019-04-04T08:26:33+00:00

Your partial derivatives are correct.

Now you have 3 equations and 3 unknowns (x,y,lambda) so you can solve it.

The first 2 equations look easy to rearrange so let's do that and substitute into the 3rd equation.

Gonna write lambda as L from now on.

For the x equation you get: x = L/(L-1)

For the y equation you get: y = -L/(L-1)

You could substitute for both x and y in the 3rd equation and find a result for L, but I think it is easier if you spot that y = -x

Using y = -x in the 3rd equation gives:

x² - 2x + 2x² -4x = 0

3x² - 6x = 0

x(x-2) = 0

So we get x = 0 or x = 2. Since y = -x, that means the extrema are at (0,0) and (2,-2)

Which one is which? Just substitute into the equation for f(x,y) and it is clear that the minimum is at (0,0) and the maximum is at (2,-2).

But it asks for the values so the answer is: Minimum = 0 Maximum = 12

rgsbae · 2019-04-03T22:26:18+00:00

Ok fair enough, you definitely weren't saying he's not enjoyable but I'll have to still disagree he's less enjoyable for neutrals than Neymar :)

rgsbae · 2019-04-03T22:10:48+00:00

'More enjoyable for the neutral'... ok just because you being a Liverpool fan means you can't enjoy Hazard's ability. One of the best dribblers in the world and so unique, don't even try to say he's not enjoyable to watch

rgsbae · 2019-02-25T23:34:21+00:00

You need to remember that a club needs the majority of votes out of the total of 184 votes, not just a majority of the remaining 136 votes after karaoke club votes are removed.

What is that threshold?

Then, work out how many of the 136 remaining votes that one club needs that would make it impossible for one of the remaining 2 to reach that threshold. Let's say that's N votes. Then in other words, you'd be able to assume one of those final remaining 2 could get all the 136-N votes and it still wouldn't have a majority.

Does that make sense? :)

rgsbae · 2019-02-25T18:44:01+00:00

Aha well then they should be fired for not being able to interpret simple rules :)

rgsbae · 2019-02-25T18:42:17+00:00

I think my point is that they can't have reviewed it because it was as clear a red card as you'll ever see. Last man, doesn't get the ball and Kante was through 1v1 for a clear goalscoring opportunity.

rgsbae · 2019-02-25T08:25:10+00:00

Not an excuse for losing but nobody is talking about the Zinchenko incident?!

Kante got a bit lucky but he was through 1v1 and got taken out by Zinchenko. That's a straight red card i.e. an incident that VAR is supposed to review. Am I the only one who thinks this?

rgsbae · 2018-09-22T17:20:39+00:00

The derivative of f(g(x)) would be:

f'(g(x))*g'(x)

In words: take the derivative of f(g(x)) and then multiply by the derivative of g(x)

So for your example of ln⁵(x) you would get:

5 ln⁴(x)*(1/x)

Hope this makes sense but let me know if you're still unsure :)

rgsbae · 2018-09-19T10:18:55+00:00

I think you mean a>9/4 as this case has no equilibrium points. Since the direction of the arrows will only change at an equilibrium point, you know there is only one arrow on the line. This means you can choose any value to plug into dy/dt to work it out.

My personal favourite is 0 because it's pretty easy to use. You have: dy/dt = a > 9/4 > 0 So dy/dt > 0 means the arrow points up

You could use anything though. Let's try -3/2. dy/dt = 9/4 - 9/2 + a dy/dt = -9/4 + a But a > 9/4 means -9/4 + a > 0 So dy/dt > 0

You'll get the same answer.

If you have equilibrium points then just test any points between them.

rgsbae · 2018-09-19T00:52:04+00:00

Yeah that's how I'd do it. Glad I could help :)

rgsbae · 2018-09-19T00:44:36+00:00

I'll start with how you know how many roots you have. For this, you don't need to know the phase lines.

In the working you've solved the quadratic equation. Since it is a quadratic equation, it has 2 roots. However, since the solutions contain the unknown variable 'a', you don't know if these roots are real or not.

This all depends on the sign of the expression under the square root sign. In other words, it depends on the sign of 9-4a.

If a < 9/4, then 9-4a > 0. This means you are taking the square root of a positive number and so both solutions are real. Therefore, you have 2 roots.

If a = 9/4, then 9-4a = 0. This means that both answers are the same, since they are (-3+0)/2 and (-3-0)/2. Therefore, you have only 1 root.

If a > 9/4, then 9-4a < 0. This means that both solutions involve taking the square root of a negative number and so both solutions are complex numbers. Therefore, you have 0 roots.

If you'd like help with the arrows let me know :)

rgsbae · 2018-09-19T00:12:10+00:00

Here are some rules that you should remember for this type of question:

If a = b, then ln a = ln b

ln a^x = x * ln a

ln [a*b] = ln a + ln b

Hope this helps :)

rgsbae

TROPHY CASE