Shelves almost empty of baby formula bear signs advising of a limit of eight cans per customer at a supermarket in Sydney on Nov. 12, 2015. (Christopher Pearce/Getty Images)

After Mandy Santos’s teething 8-month-old son woke her every two hours one night demanding to be fed, she walked into a Sydney supermarket looking for a can of baby formula.

As the 31-year-old professional violinist stood in the baby-food aisle trying to choose a product, her 2-year-old daughter hung on to her leg, chewing on a cookie. The little boy was with a relative.

“He’s very clingy and I’m too tired,” Santos said, referring to the baby. “I’m going to wean him slowly.”

But there was a catch: Despite fully stocked shelves of formula made by Procter & Gamble, Nestlé, Danone and others, this supermarket in the Coles chain sells only two cans to a customer at a time. The rule is aimed at countering a thriving underground market that ships Australian formula to China, where only 16 percent of new mothers breast-feed their children exclusively, according to China’s National Health and Family Planning Commission.

Private profiteers can resell a two-pound can of formula in China for as much as three times the Australian price, said Michael Harvey, a dairy-industry analyst at Rabobank, a large agricultural financier. “There is clearly money in it,” he said in an interview.

Several milk-contamination scandals, including one that involved the hospitalization of 54,000 children in 2008, have made many in China suspicious of their food supply. The one-child policy, which is now being abandoned, also made many of the 16 million babies born every year in China even more precious to their parents.

Experts say Chinese food rules are as tough as Australia’s — they are both based on international standards known as the Codex Alimentarius, overseen by the World Health Organization and the U.N. Food and Agriculture Organization. But many Chinese parents do not trust their government to enforce the rules.

“The Chinese consumer wants the formula with the English writing on it,” said Jan Carey, the chief executive of Australia’s Infant Nutrition Council, a lobby group for baby-food makers.

Australia is not the only place where sales limits have been imposed. Britain, Hong Kong and New Zealand also have them, but the problem is more acute in Australia. The country’s clean environment and reputation for safe food appeals to Chinese parents, said Simon Hansford, a formula consultant who has been to China more than 80 times and once owned a milk-powder factory.

“They love their Louis Vuitton and BMWs,” he said in an interview. “They think if the formula is sold in the big supermarkets and pharmacies, it’s a famous brand.”

While well-intentioned, the Australian supermarkets’ policy means the country’s exhausted mothers have to stock up every couple of weeks or seek out stores with more generous limits. At the Coles visited by Santos, the violinist, a notice in English and Chinese said: “While this is regrettable we are trying to help make this product available for our customers who require it.”

The rule is not always enforced. Two months ago, a woman from the southern city of Melbourne posted a photo on Facebook of four people filling two shopping carts with baby formula. “The group of four adults cleared a pallet of more than 50 tins despite the store’s four-tins-per-person limit,” she told the Sydney Morning Herald newspaper. “It felt like a smooth operation, like they did this all the time.”

Chinese buyers send the formula home by regular mail, a process that does not require special paperwork if the shipment weighs less than 22 pounds. Reports that temporary shops are opening in busy areas to sell and ship formula suggest that the trade is becoming more sophisticated.

A spokeswoman for Australia’s Department of Agriculture and Water Resources said the agency is investigating allegations that formula is being sent overseas in breach of shipping rules.

Ironically, most of the formula sold in Australia comes from elsewhere. The most popular brand, Aptamil, is made by French dairy giant Danone in New Zealand, a country that has so many cows it is sometimes referred to as the “Saudi Arabia of the global milk trade.” In China, Danone sells formula under the Karicare brand, which it promotes as a 100 percent New Zealand product.

Breast-feeding advocates are aghast at the trade, which they say preys on vulnerable women in China. Nina Berry, a researcher at the Sydney School of Public Health and a spokeswoman for the Australian Breastfeeding Association, described the prices being paid for foreign formula in China as “extortionate” and questioned the ethics of food companies that market the products. Some experts want China to ban the advertising of baby formula.

Women with infants are “doing very undervalued work, with very little support, often in isolation and unable to access the personal support, professional advice or industrial protections they need,” Berry said in an email.

The baby-formula industry is acutely aware of the criticism and says children should be breast-fed for their first six months. Privately, industry advocates say many Chinese mothers choose formula so they can return to work quickly and save money to fund their children’s education.

Seeing the opportunity, Australian manufacturers are scrambling to meet demand. But the adjustment is not happening quickly. It takes some six months to increase production, because ingredients such as vegetable fat and vitamins have to be ordered well in advance.

Nonetheless, investors sense big profits. Baby-food makers more generally were among the most successful companies on the Australian stock exchange last year. A $5,000 investment in one company, Bellamy’s Organic, on Jan. 1 last year was worth $49,000 by New Year’s Eve, according to CommSec, a stockbroker.

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Today’s coverage from Post correspondents around the world