用$1$块$A$型钢板可恰好制成$2$块$C$型钢板和$1$块$D$型钢板；用$1$块$B$型钢板可恰好制成$1$块$C$型钢板和$3$块$D$型钢板.
$(1)$若需$14$块$C$型钢板和$12$块$D$型钢板,则恰好用$A$型钢板、$B$型钢板各多少块?
$(2)$现准备购买$A$、$B$型钢板共$50$块,并全部加工成$C$、$D$型钢板,要求$C$型钢板不超过$86$块,$D$型钢板不超过$90$块,求$A$、$B$型钢板的购买方案共有多少种?
$(3)$在（2）的条件下,若出售$C$型钢板每块利润为$100$元,$D$型钢板每块利润为$120$元,则全部售出$C$、$D$型钢板可获得的最大利润为______元.