Maxima and Minima

Calculus Level 5

Subject to x+y=1x+y=1 for positive reals, the maximum and local minimum of x4y+y4x x^4 y + y^4 x can be expressed as ab \frac{a}{b} and cd \frac{c}{d}, respectively, where a,ba,b and c,dc,d are pairs of positive coprime integers.

Find a+b+c+da+b+c+d.

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