The Town of Intolerance Decides to Ban the Outdoor Advertising

The town of Intolerance decides to ban the outdoor advertising of alcohol in media such as billboards. Establishments selling or serving alcohol may have on-site outdoor signs identifying the business, and may include alcohol-related terms in their name, such as "The Liquor Store," but may not have outdoor displays identifying the brands of alcohol or the price of alcohol sold. The city claims that these measures will reduce alcohol consumption and thereby reduce alcohol-related problems, such as drunk driving. A brewery and a bar challenge this law as a violation of the First Amendment. The brewery wants to advertise the "fresh, natural taste" of its beer. The bar wants to advertise the brands and prices of beer it sells. Is this ordinance constitutional? In your answer, apply the Central Hudson test, and relevant precedents, to this ordinance.