The member countries of the World Health Organization (WHO) have recently endorsed its Global Strategy on Diet, Physical Activity and Health. The strategy emphasizes the need to limit the consumption of saturated fats and trans fatty acids, salt and sugars, and to increase consumption of fruits and vegetables in order to combat the growing burden of non communicable diseases. Adherence to the norms recommended by the WHO would call for major changes in the consumption, production and trade of several key food products and several sectors of the food industry have expectedly raised serious concerns about the potential impact of these norms on their future growth prospects. This paper attempts a broad quantitative assessment of the consumption impacts of these norms in OECD countries using a mathematical programming approach. We find that adherence to the WHO norms would involve a significant decrease in the consumption of vegetable oils (30%), dairy products (28%), sugar (24%), animal fats (30%) and meat (pig meat, 13.5%, mutton and goat 14.5%) and a significant increase in the human consumption of cereals (31%), fruits (25%) and vegetables (21%). The paper also explains the apparent dilemma that some OECD countries face when simultaneously trying to liberalise agricultural markets and promote healthy diets.