An urban greenhouse produces and sells seedlings in complete batches of 1000. Let $q$ be the number of batches produced in a year, where $q$ is an integer and $0\leq q\leq80$

The selling price per seedling is modelled by

$$p(q)=96-1.2q$$

dollars. The annual operating cost is modelled by

$$C(q)=0.4q^2+12q+500$$

thousand dollars. The greenhouse also pays an annual permit fee of $F$ thousand dollars. Assume that all seedlings produced are sold.

Let $P_F(q)$ denote the annual profit, in thousands of dollars. The greenhouse considers a year acceptable if its profit is at least $350 000.