A foundry$8$ is developing a long$-$range strategic plan for buying scrap metal for its operations. The foundry

can buy scrap metal in unlimited quantity from two sources: Atlanta and Birmingham, and it receives the

scrap daily by railroad cars.

The scrap is melted down, and lead and copper are extracted. Each railroad car from Atlanta yields $1$ ton of

copper and $1$ ton of lead, and costs $$10,000.$ Each railroad car from Birmingham yields $1$ ton of copper and

$2$ tons of lead, and costs $$15,000.$ The foundry needs at least $4$ tons of lead and at least $2\mathrm{.}5$ tons of copper

per day for the foreseeable future.