In a previous paper, [1] it was shown that a solution, f(x) will exist for the optimal inventory equation (where f(y − z) = f(0), y < z) provided:

1. 1. g(x) ≧ 0, x ≧ 0;

2. 2. 0 < a < 1;

3. 3. h(x) is monotonically nondecreasing, h(0) = 0;

4. 4. F is a distribution function on [0, ∞);

   (In [1], 1–4 were denoted collectively as (A).)

   and either

5. 5a. g(x) is continuous for all x ≧ 0;

6. 5b. lim x→∞ g(x) = ∞;

7. 5c h(x) is continuous for all x > 0 (Theorem 2 of [1]);

   or

8. 6. g(x) is uniformly continuous for all x ≧ 0 (Theorem 3 of [1]).