How to solve the cattle pen problem?

K

konchober2019-10-30 00:07:14

Mathematics

konchober, 2019-10-30 00:07:14

Task from the book Theoretical Minimum in Computer Science. Everything a programmer and developer needs By Vladston Ferreira Filo

https://books.google.ru/books?id=m6JSDwAAQBAJ&pg=P...
The conditions are clear:

A = w * l
100 = 2w + 3l

But I can’t understand how he derives the following formulas and how to solve the problem and get an answer in the end. He writes that it is easily solved using the formula of the roots of a quadratic equation.
Googled what the formula is:

Формула дискриминанта Дискриминант D квадратного трёхчлена ax2 + bx + c равен b2 - 4ac.

But I don't see any connection to this problem...

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2 answer(s)

R

Rsa97, 2019-10-30
@Rsa97

^{Classically, problems} for extrema of functions are
solved
through derivatives : 50/3 = 16.(6) A''(50/3) = -3 < 0 => maximum point w = 25 But it is also possible through a quadratic equation: A = 50l - (3/2)l ² = 0 D = 50 ² l ₁ = (-50 + sqrt(D)) / (2 * (-3/2)) = 0 l ₂ = (-50 - sqrt(D)) / (2 * (-3/2) ) = 100/3 For a quadratic equation, the extremum point lies in the middle between the roots l = (l ₁ + l ₂ ) / 2 = 50/3 w = 25
Algebra, 8-9-10 grades.

L

longclaps, 2019-10-30
@longclaps

The problem of finding the maximum involves the calculation of the derivative.
You can google what it is)