First, since is an increasing function, any maximum value of is a maximum value of x so it is sufficient to maximize . Taking, as constraint, x+ y+ z= 2p, a constant, you want to maximize F(x, y, z)= p(p- x)(p- y)(p- z) with constraint G(x, y, z)= x+ y+ z= 2p. You want to find x, y, z such that for some constant . Don't forget that p is a constant.