0
votes
1answer
28 views

How do I find the critical values to find the maximum of this function?

The total daily profit in dollars realized by the TKK Corporation in the manufacture and sale of x dozen recordable DVDs is given by the total profit function below. $$P(x) = −0.000001x^3 + 0.001x^2 + ...
2
votes
1answer
77 views

Generalization of Erdős-Ko-Rado where intersections have cardinality in given set

Problem: Let $T\subseteq \{0,\ldots, k-1\}$ and let $\mathcal F\subseteq [n]^{(k)}$ (subsets of size $k$) such that $|A\cap B|\in T$ for $A,B\in \mathcal F$, $A\ne B$. Show that if $n\ge ...
-2
votes
1answer
42 views

Min $A=14(a^{2}+b^{2}+c^{2})+\frac{ab+bc+ac}{a^{2}b+b^{2}c+c^{2}a}$?

$a;b;c\in \mathbb{R}^+$ such that $a+b+c=1$. Find the minimum of $A=14(a^{2}+b^{2}+c^{2})+\frac{ab+bc+ac}{a^{2}b+b^{2}c+c^{2}a}$
0
votes
2answers
81 views

Bounds for maximal blowup contained in graph

In my homework, I'm asked to prove the following: By denoting $b_n(r,\epsilon)$ - the largest integer $b$ so that any graph with $(1-\frac{1}{r} +\epsilon)\frac{n^2}{2}$ edges, contains a $b$-blowup ...
5
votes
1answer
253 views

Graph with 10 nodes and 26 edges must have at least 5 triangles

This is not a homework question, but I would appreciate if people would treat this as if it were homework. I am looking for (nonspoiler) hints. I would like to prove that given any graph with 10 ...