Table 1. Specific scenarios used for the optimization modeling with a focus on achieving nutrient levels at lowest cost along with low GHG emissions.

Aim of specific scenario	Additional details on the constraints*
Minimizing cost while meeting nutritional requirements
C1) To minimize food cost (while meeting nutrient requirements).	To achieve all the recommended daily energy and nutrient levels (Table S2 in File S1) while minimizing cost. We also limited added sugar to no more than 60 g/d which is half the usual total intake for NZ males).
C2) As per Scenario C1 but to allow(i) a standard porridge dish; and(ii) the flour to be mixed withvegetable oil to make rotis	We required that the flour be considered in conjunction with the inclusion of vegetable oil (at a 7∶1 ratio of flour to vegetable oil). Two cups of flour (240 g) makes around 8–10 rotis, each 10 cm in diameter. Minimal salt in cooking to fall within the nutrient constraints = 0.5 teaspoon (3 g). (We note various alternatives to using the flour in rotis: e.g., scones, damper, tortillas etc. Versions of Cornish pasties and samosas can also be prepared from flour and vegetables.). We included a standard porridge dish at breakfast of ¼ cup (≥39 g) of whole grain oats and ¾ cup of milk made from ≥25 g skim milk powder (where 1 kg makes 10 liters of milk). Minimal salt used in cooking = 0.25 teaspoon (1.5 g).
C3) As per Scenario C1 but requiring very minimal cooking skills	It was assumed that cooking skills were limited to cooking pasta, canned foods, rice and vegetables. The “food skills constraint” ruled out the cooking of: flour (all types), lentils, semolina, couscous and dried peas.
C4) As per Scenario C1 but withextra fruit and vegetables at lowestpossible cost	The additional requirement was for the diet to reach ≥75% of the average intake of vegetables for men consuming a Mediterranean-style diet [21] (i.e., ≥412 g [549 g for men ×75%]). The maximum level for any particular vegetable was set at 200 g, and we excluded starchy root crops (potatoes, kumara and taro) and juices.
Minimizing GHGs while meeting nutritional requirements
G1) To minimize greenhouse gas(GHG) emissions (while achievingthe nutrient levels).	To keep cost to <NZ$ 5 per day.
G2) As above but for a highercost per day	To keep cost to <NZ$ 9/d.**
G3) As per Scenario G2 but with porridge as a standard feature	As per the <$9/d constraint**, but with the porridge and skim milk (as per Scenario C2) included).
G4) As per G2 but fully vegan	As per the <$9/d constraint**, but with exclusions on milk and other dairy products, eggs, fish and all other meat (i.e., vegan).

^*In all scenarios (Table 1 and Table 2) we set daily maximum limits for flour, pasta and oats (each at 240 g), no more than 200 g of any particular vegetable (including fresh, frozen, and canned vegetables), and adjusted added salt to ensure that total sodium intake stayed below maximum recommended levels, as per Table S2 in File S1. All the weights in this table are for prepared ready-to-eat items, with purchased weights assumed to be higher due to inedible portions such as skins and spoiled parts – with these wastage proportions obtained from the USDA database) [57]. A lower limit of 10 g applied to all ingredients except condiments such as sugar and salt, and ingredients that were specified in the recipes, e.g., 8 g wholemeal flour in Scenario NZ-M.).

^**We based this on an annual survey (the University of Otago “Food Cost Survey”) where for 2011 the calculated costs for a “basic diet” were $9.29/d for men and $8.71/d for women [41].