Identification of nutritionally adequate mixtures of vegetable oils by linear programming N. Darmon,* M. Darmon & E. Fergusonà *National Institute of Health and Medical Research, INSERM, Paris, France;  Nutrition Research Unit, Marseille Cedex, France; àDepartment of Human Nutrition, University of Otago, Dunedin, New Zealand Introduction Dietary intakes of fats are important determinants of health, especially cardiovascular health (WHO- FAO, 1994). Saturated fatty acids (SFA) and trans- fatty acids elevate plasma cholesterol concentra- tion and the risk of coronary heart diseases, whereas monounsaturated and polyunsaturated fatty acids have the opposite effect (Hu et al., 1997). Among the polyunsaturated fatty acids, only linoleic acid (LA; C18:2 n-6), the precursor of arachidonic acid and other x-6 fatty acids, and a- linolenic acid (ALA; C18:3 n-3), the precursor of docosahexaenoic acid (DHA), eicosapentaenoic acid (EPA) and other long chain x-3 fatty acids, are indispensable for humans. Prospective cohort studies (Ascherio et al., 1996; Hu et al., 1999) and secondary prevention trials (de Lorgeril et al., Ó The British Dietetic Association Ltd 2006 J Hum Nutr Dietet, 19, pp. 59–69 59 Correspondence Nicole Darmon, Nutrition Research Unit 476 INSERM/ 1260 INRA, 27 Bd Jean Moulin, 13385 Marseille Cedex 05, France. Tel.: +33 4 91 29 40 97 Fax: +33 4 91 78 21 01 E-mail: nicole.darmon@medecine.univ- mrs.fr Keywords a-linolenic acid, dietary recommendations, linear programming, vegetable oils, vitamin E. Abbreviations AFSSA, French Food Safety Agency; ALA, a-linolenic acid; ANC, Apports Nutritionnels Conseille ´s; DHA, docosahexaenoic acid; EPA, eicosapentaenoic acid; LA, linoleic acid; LPM, linear programming mixtures; MUFA, monounsaturated fatty acids; SFA, saturated fatty acids. Abstract Objective To determine the types and proportions of vegetable oils to recommend for a healthy diet. Methods Optimal vegetable oil combinations were designed, using linear programming and, as decision variables, nine single oils and 29 basic food items. ‘Oil models’ were run to determine whether rea- sonable amounts of individuals oils or oil mixtures satisfied a set of constraints on essential fatty acids and vitamin E. ‘Meal models’ were run to test whether selected mixtures could be used as the sole source of added fat in a meal that met micronutrient and macronutrient recommendations. Results The cheapest mixture (0.97 € L )1 ) that solved the oil models contained 81% rapeseed and 19% sunflower oils. About 10– 15 g of this mixture, alone or with olive, soya bean, wheat germ or walnut oils, also solved the meal models. Mixtures that contained a high proportion (‡50%) of the tasty olive and walnut oils also solved the models but were more expensive (4.9 € L )1 and 8.5 € L )1 , respectively). Conclusions The consumption of a mixture composed of rapeseed and sunflower oils in a 4 : 1 proportion is an inexpensive and simple way to meet current dietary recommendations for essential fatty acids and vitamin E, favouring overall dietary nutrient adequacy.