MathDB

14

Part of 2011 Math Prize For Girls Problems

Problems(1)

Math Prize 2011 Problem 14

Source:

9/19/2011
If 0≤p≤10 \le p \le 1 and 0≤q≤10 \le q \le 1, define F(p,q)F(p, q) by F(p,q)=−2pq+3p(1−q)+3(1−p)q−4(1−p)(1−q). F(p, q) = -2pq + 3p(1-q) + 3(1-p)q - 4(1-p)(1-q). Define G(p)G(p) to be the maximum of F(p,q)F(p, q) over all qq (in the interval 0≤q≤10 \le q \le 1). What is the value of pp (in the interval 0≤p≤10 \le p \le 1) that minimizes G(p)G(p)?
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