これにはおそらく、いくつかのサブクエリを結合する必要があります。
これはテストされていません(テーブル定義もテストデータもないため)が、次のようなものです:-
SELECT i.name AS ingredient,
ip.price,
ip.date,
s.name AS storename,
b.name AS brandname
FROM ingredient i
INNER JOIN ingredient_price ip
ON ingredient.ingredient_id = ingredient_price.ingredient_id
INNER JOIN store_to_ingredient_price stip
ON ingredient_price.ingredient_price_id = store_to_ingredient_price.ingredient_price_id
INNER JOIN store s
ON store_to_ingredient_price.store_id = store.store_id
INNER JOIN brand_to_ingredient_price btip
ON ingredient_price.ingredient_price_id = brand_to_ingredient_price.ingredient_price_id
INNER JOIN brand b
ON brand_to_ingredient_price.brand_id = brand.brand_id
INNER JOIN
(
SELECT i.ingredient_id,
stip.store_id,
ip.date,
MIN(ip.price) AS lowest_price
FROM ingredient i
INNER JOIN ingredient_price ip
ON ingredient.ingredient_id = ingredient_price.ingredient_id
INNER JOIN store_to_ingredient_price stip
ON ingredient_price.ingredient_price_id = store_to_ingredient_price.ingredient_price_id
INNER JOIN
(
SELECT i.ingredient_id,
stip.store_id,
MAX(ip.date) AS latest_date
FROM ingredient i
INNER JOIN ingredient_price ip
ON ingredient.ingredient_id = ingredient_price.ingredient_id
INNER JOIN store_to_ingredient_price stip
ON ingredient_price.ingredient_price_id = store_to_ingredient_price.ingredient_price_id
GROUP BY ingredient_id, store_id
) Sub1
ON i.ingredient_id = Sub1.ingredient_id
AND stip.store_id = Sub1.store_id
AND ip.date = Sub1.latest_date
GROUP BY i.ingredient_id, stip.store_id, ip.date
) Sub2
ON i.ingredient_id = Sub2.ingredient_id
AND stip.store_id = Sub2.store_id
AND ip.date = Sub2.date
AND ip.price = Sub2.lowest_price