解:?$(1)①$?當(dāng)購進(jìn)?$A$?和?$B$?兩種型號(hào)手機(jī)時(shí)
設(shè)購進(jìn)?$A$?型號(hào)手機(jī)?$a$?臺(tái),則購進(jìn)?$B$?型號(hào)手機(jī)?$(50-a)$?臺(tái)
根據(jù)題意得?$1500a+2100(50-a)=90000$?,解得?$a=25$?
故可購進(jìn)?$A$?型號(hào)手機(jī)?$25$?臺(tái),購進(jìn)?$B$?型號(hào)手機(jī)?$25$?臺(tái)
?$ ②$?當(dāng)購進(jìn)?$B$?和?$C$?兩種型號(hào)手機(jī)時(shí)
設(shè)購進(jìn)?$B$?型號(hào)手機(jī)?$b$?臺(tái),則購進(jìn)?$C$?型號(hào)手機(jī)?$(50-b)$?臺(tái)
根據(jù)題意得?$2100b+2500(50-b)=90000$?,解得?$b=87.5>50$?,故舍去
?$③$?當(dāng)購進(jìn)?$A$?和?$C$?兩種型號(hào)手機(jī)時(shí)
設(shè)購進(jìn)?$C$?型號(hào)手機(jī)?$c_{臺(tái)}$?,則購進(jìn)?$A$?型號(hào)手機(jī)?$(50-c)$?臺(tái)
根據(jù)題意得?$1500(50-c)+2500c=90000$?,解得?$c=15$?
故可購進(jìn)?$C$?型號(hào)手機(jī)?$15$?臺(tái),購進(jìn)?$A$?型號(hào)手機(jī)?$35$?臺(tái)
故有兩種進(jìn)貨方案 方案一:可購進(jìn)?$A$?型號(hào)手機(jī)?$25 $?臺(tái),購進(jìn)?$B$?型號(hào)手機(jī)?$25$?臺(tái);
方案二:可購進(jìn)?$C$?型號(hào)手機(jī)?$15$?臺(tái),購進(jìn)?$A$?型號(hào)手機(jī)?$35$?臺(tái)
?$(2)$?方案一的利潤(rùn):?$25×(1650-1500)+25×(2300-2100)=8750($?元?$)$?
捐款數(shù)額:?$8750×50\%=4375($?元?$)$?;
方案二的利潤(rùn):?$15×(2750-2500)+35×(1650-1500)=9000($?元?$)$?
捐款數(shù)額:?$9000×50\%=4500($?元?$)$?
∵?$4375<4500$?
故選擇方案二,即購進(jìn)?$C$?型號(hào)手機(jī)?$15$?臺(tái),購進(jìn)?$A$?型號(hào)手機(jī)?$35$?臺(tái),可以使捐款最多