The profit (in thousand rupees) from producing and selling a certain item is modelled by the polynomial P(x)=−x2+9x−18, where x represents the number of units produced (in hundreds).
(i) Test whether x=3 and x=6 make the profit zero.
(ii) Explain the practical meaning of each zero obtained in part (i) with respect to the production level.
(iii) Using the zeros, sketch a rough graph of y=P(x) against x and indicate the intervals in which the profit is positive and negative.