Min - Elements

Query
public void Linq84()
{
List products = GetProductList();

var categories =
from p in products
group p by p.Category into g
let minPrice = g.Min(p => p.UnitPrice)
select new { Category = g.Key, CheapestProducts = g.Where(p => p.UnitPrice == minPrice) };

ObjectDumper.Write(categories, 1);
}
Lambda Expression
public void Linq84()
{
List products = GetProductList();

var categories = products.GroupBy(prod => prod.Category).
Select(prodGroup => new {prodGroup, minPrice = prodGroup.Min(p => p.UnitPrice)}).
Select(@t => new {
Category = @t.prodGroup.Key,
CheapestProducts = @t.prodGroup.Where(p => p.UnitPrice == @t.minPrice)});

ObjectDumper.Write(categories, 1);
}
Output
Category=Beverages CheapestProducts=...
CheapestProducts: ProductID=24 ProductName=Guaraná Fantástica Category=Beverages UnitPrice=4.5000 UnitsInStock=20
Category=Condiments CheapestProducts=...
CheapestProducts: ProductID=3 ProductName=Aniseed Syrup Category=Condiments UnitPrice=10.0000 UnitsInStock=13
Category=Produce CheapestProducts=...
CheapestProducts: ProductID=74 ProductName=Longlife Tofu Category=Produce UnitPrice=10.0000 UnitsInStock=4
Category=Meat/Poultry CheapestProducts=...
CheapestProducts: ProductID=54 ProductName=Tourtière Category=Meat/Poultry UnitPrice=7.4500 UnitsInStock=21
Category=Seafood CheapestProducts=...
CheapestProducts: ProductID=13 ProductName=Konbu Category=Seafood UnitPrice=6.0000 UnitsInStock=24
Category=Dairy Products CheapestProducts=...
CheapestProducts: ProductID=33 ProductName=Geitost Category=Dairy Products UnitPrice=2.5000 UnitsInStock=112
Category=Confections CheapestProducts=...
CheapestProducts: ProductID=19 ProductName=Teatime Chocolate Biscuits Category=Confections UnitPrice=9.2000 UnitsInStock=25
Category=Grains/Cereals CheapestProducts=...
CheapestProducts: ProductID=52 ProductName=Filo Mix Category=Grains/Cereals UnitPrice=7.0000 UnitsInStock=38
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