does anyone know how to do this
find x and z that maximizes ln(4-x) + ln(4+z) + ln(z)
2 lnx + ln(4-z) + ln(4-z) = 2ln(32/7)
anyhelp is much appreciated
as x>0, the constraint may be rewritten:
So substitute (2) into (1) and find the z that maximises this now
unconstrained objective, find the corresponding x from 2, and substitute
back into ln(4-x) + ln(4+z) + ln(z) to find its maximum.
g(x,z)=ln( (4-x)(4+x)x )
by the law of logarithms.
and because the exponential function is increasing on the real numbers, any
maxima of g(x,z) is also a maxima of f(x,z) and vice-versa.