micro-economia optimizatció de una esfera

B(r) = (1/10pi)·(4pi)·( p·r^{2}+(-1)·m·(1/3)·r^{3} )


d_{x}[B(r)] = 2p·r+(-1)·m·r^{2}


mr = 2p


r = ( (2p)/m )


B( (2p)/m ) = (4pi)( (2/3)(p^{3}/m^{2}) )


pelota de tenis:


p=3 &  m=2


B(3) = (1/10pi)·(18pi) = 1.8€
B(r) = (1/10pi)·( F(r)+(-1)·V(r) )
(1/10pi)·F(3)  = 2.7€
(1/10pi)·V(3) = 0.9€