2011 MPFG Problem 14: Difference between revisions
Created page with "==Problem== If <math>0 \leq p \leq 1</math> and <math>0 \leq p \leq 1</math>, define <math>F(p,q)</math> by <math>F(p,q) = -2pq + 3p(1-q) + 3(1-p)q-4(1-p)(1-q)</math>. Define..." |
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We can view the problem from a geometric meaning. | We can view the problem from a geometric meaning. | ||
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<math>F(p,q) = -2A + 3B + 3C - 4D = 3(1-A-D) - 2A - 4D = -5A - 7D + 3</math> | <math>F(p,q) = -2A + 3B + 3C - 4D = 3(1-A-D) - 2A - 4D = -5A - 7D + 3</math> | ||
Latest revision as of 04:08, 23 August 2025
Problem
If 
and , define 
by 
. Define 
to be the maximum of over all 
(in the interval 
). What is the value of 
(in the interval ) that minimizes ? Express your answer as a fraction in simplest form.
Explanation
We can view the problem from a geometric meaning.
