33. Using 1 piece of type $A$ steel plate can produce 2 pieces of type $C$ steel plate and 1 piece of type $D$ steel plate; using 1 piece of type $B$ steel plate can produce 1 piece of type $C$ steel plate and 3 pieces of type $D$ steel plate. Now, it is planned to purchase a total of 100 pieces of type $A$ and $B$ steel plates, and process them all into type $C$ and $D$ steel plates. It is required that there are no fewer than 120 pieces of type $C$ steel plates and no fewer than 250 pieces of type $D$ steel plates. Let the number of type $A$ steel plates purchased be $x$ (where $x$ is an integer).
(1) There are $\qquad$ purchasing plans;
(2) The profit from selling each piece of type $C$ steel plate is 100 yuan, and the profit from selling each piece of type $D$ steel plate is 120 yuan. If all type $C$ and $D$ steel plates are sold, then the profit is maximized when purchasing $\qquad$ pieces of type $A$ steel plates.
answer: 6,20