He wants to open a restaurant in which men will mix with women
Question

I want to open a restaurant in one of the Muslim countries where men and women mix and most people live a western kind of lifestyle. Will I be sinning if some of these people who mix come to eat in my restaurant? Please take into consideration that this is work that I can do in the best manner.
Praise be to Allah.So long as this country is one in which men mix with women and most people live a western kind of lifestyle, this means that in this restaurant there will be a number of objectionable issues: 
1.Women showing their adornment and charms without any religious or moral deterrent.
2.Free mixing between men and women, which leads to a great deal of immorality.
3.Haraam and dubious relationships among the customers of the restaurant, such as a man coming with his girlfriend to this restaurant.
 These matters -- as is well known -- are haraam and are things that pose the greatest danger to society. 
Ibn al-Qayyim (may Allah have mercy on him) said: 
There is no doubt that enabling women to mix with men is the basis of all calamity and evil, and it is one of the greatest causes of all-encompassing punishment coming down. It is also one of the causes of corruption in public and private affairs. Mixing of men and women is the cause of a great deal of immoral actions and zina. And it is one of the causes of widespread death and ongoing plagues. 
One of the greatest causes of widespread death is the prevalence of zina, because of enabling women to mix with men and walk among them displaying their finery and beautified. If the people in charge knew how much corruption that causes in worldly affairs and people’s affairs, let alone religious affairs, they would be stricter in putting a stop to it. End quote. 
Al-Turuq al-Hukmiyyah, p. 407-408 
Just as Allah has forbidden disobedience to Him, He has also forbidden helping the sinner in his disobedience, and has made it obligatory to stop him from committing that sin. 
Allaah says (interpretation of the meaning):
“Help you one another in Al‑Birr and At‑Taqwa (virtue, righteousness and piety); but do not help one another in sin and transgression. And fear Allaah”
[al-Maa’idah 5:2]
And Muslim (49) narrated from Abu Sa‘eed al-Khudri (may Allah be pleased with him) that the Prophet (blessings and peace of Allah be upon him) said: 
“Whoever among you sees an evil action, then let him change it with his hand [by taking action]; if he cannot, then with his tongue [by speaking out]; and if he cannot, then with his heart – and that is the weakest of faith.” 
Al-Nawawi (may Allah have mercy on him) said: 
The words of the Prophet (blessings and peace of Allah be upon him), “let him change it,” is a command according to the consensus of the ummah, and the obligation of enjoining what is good and forbidding what is evil, is well established according to the Qur'aan and Sunnah and the consensus of the ummah. This is also part of the sincerity (naseehah) which is Islam. End quote. 
So it is not permissible for the Muslim to help the sinner in his sin. Opening this restaurant in the way you described involves helping these people in their deviance and keeping quiet about their evil deeds and falsehood. 
Seeing that you cannot prevent these evils and you will rather be helping people in committing them, our advice to you is to forget about this work and look for something else. Remember that “Whoever gives up a thing for the sake of Allah, Allah will compensate him with something better than it,” and “And whosoever fears Allaah and keeps his duty to Him, He will make a way for him to get out (from every difficulty). 3. And He will provide him from (sources) he never could imagine” [al-Talaaq 65:2-3]. 
We ask Allah to make things easy for you and to grant you a good, halaal provision. 
And Allah knows best.