Ferrous scrap (from shredded cars, old appliances, etc.) is one of the
major inputs into steel making.  Ferrous scrap prices have increased
significantly in the past two years (depends on the grade, but most
look like they've increased 2-3x in price).

My question is:

When making steel using a Basic Oxygen Furnace (BOF) (usually in an
old-style, integrated steel mill), the Ferrous scrap can range from
10% - 30% of the 'input materials' for making the steel.

What relative prices and calculations or constraints will a steel
maker look at when deciding whether to use 10% scrap or 30% scrap (or
somewhere in
between)?

In particular, what are the specific pieces of the relative costs
they'd look at (iron ore, electricity, additives, scrap, etc.),
current values for these costs (in the US), and a specific 'equation'
they could use to calculate what % of scrap (at a given scrap price)
gave them the lowest overall costs?

Dear bizguy123,
When u speak of BOF ( Linds Donavitz process of making steel) the main
input is the liquid iron from blast Furnaces. how much and what % of
scrap is added depends on the ingradients of the scrap and their cost
per MT and ofcourse their availability vis a vis desired Carbon % in
outputted steel.

But there is one more input to be considered, i.e., sponge iron, which
is extensively used in steel making especially in electric arc furnace
route.