Remember we say "as soon as possible" instead of "as far as possible"
at your earliest convenience means as soon as one can without difficulty.
For example: "Please telephone me at your earliest convenience."
"as far as possible"
を使う代わりに"as soon as possible"を使う事を覚えておきましょう。
"at your earliest convenience"とは、都合がつき次第なるべく早く、と言う意味です。
例: "Please telephone me at your earliest convenience."
都合がつき次第すぐに電話をください。
It's a delicate situation here because if you ask your business partner to 'do his best,' he will assume you are saying that because you believe he would not normally do his best - or perhaps something he did previously he did badly.
So you could say, "I'm sure you'll do your best." However, even that sentence seems to infer you do not really trust your partner.
In a normal situation, "I'll leave it to you," is a far more effective sentence because it gives a positive impression that you believe in your partner and are sure he will carry out the task well. If you have low expectations of people, they will pick up on that and may be offended.
We really need solid data for this project. so please give it your best shot!
"Your best shot " is an idiom that we may well find good use for in this situation;-D
It suggests "a true aim" or "strong focus" in order to get the desired outcome.
In this scenario we need the best possible effort, from an associate:
"We really need solid data for this project. so please give it your best shot!"
"Your best shot " とは、この場合使えるイディオムです。望んだ結果にするために、全力を尽くす、できるだけのことをするという意味です。
この場合、同僚の努力が必要ということになります。
"We really need solid data for this project. so please give it your best shot!"
このプロジェクトには確かなデータがすごく必要です。だから全力を尽くしてください。
南アフリカ 
イギリス 
