Question

Calc III word problem, really need help.Additional information in next post.

The Hardy-Weinberg Law states that the proportion P of heterozygous individuals in any given population is P(p,q,r) = 2pq + 2pr + 2qr where p represents the percent of allele A in the population, q represents the percent of allele B in the population, and r represents the percent of allele O in the population. Use the fact that p + q + r = 1 to show that the maximum proportion of heterozygous individuals in any population is (2/3)

Answer 1

The following text is written at the beginning of the problem:
Hardy-Weinberg Law: Common blood types are determined genetically by three alleles A, B, and O. (An allele is any of a group of possible mutational forms of a gene.) A person whose blood type is AA, BB, or OO is homozygous. A person whose blood type is AB, AO, or BO is heterozygous.

Answer 2

Have you learned Lagrange multipliers, yet?

Answer 3

I don't think so.. I zone out in class sometimes but I'm pretty sure we haven't got there yet. Right now we're on gradients

Answer 4

Then you probably should check it out, it's the way to solve this problem (using gradients).

http://en.wikipedia.org/wiki/Lagrange_multiplier

Answer 5

WAIT, I think we did go over this in class. I must have been completely zoned out lol. I do need to learn this.

Answer 6

So it has to do with the local max and min of a function, except in multiple variable sorta, right?

Answer 7

Essentially, yes. I would take some time to intuitively understand how the contours play a part in this, though, which is not quite easy if it's your first run through.

Answer 8

Oh boy, I'm not gonna get any sleep tonight lol. Thank you so much though, I will look into it. Could you give me a hint on how the lagrange multiplier applies to this pattern?

Answer 9

Er, problem

Answer 10

If you want, I can solve this problem and show all steps, but I'd recommend looking into it, carefully.

Answer 11

Actually if you could that would be very helpful. I tend to learn better just going through the problems and trying to gain an intuition afterwards hahah

Answer 12

Sounds good, also, read up on the "Lagrange Multipliers" section of this while I do the write up.

http://www.physics.miami.edu/~nearing/mathmethods/multivariable_calculus.pdf

Answer 13

Sure thing.

Answer 14

Here.

Answer 15

I actually have to afk unfortunately, but thank you SO much. That PDF is very well written and is helping me with my understanding of the other parts of multivariable calculus i was having trouble with. I have to go for now but thank you so much it is much appreciated :)

Answer 16

And of course thank you for the work

Answer 17

Sure thing.