$1.(1\mathrm{.}5$ point$)$ The cost function of a large railroad corporation is Y$=107+$T$,$ where Y is the total cost

of shipping in U$.$S$.$ dollars and T is the tons shipped.

Last year the company charged on average $1\mathrm{.}3$ dollars for each ton of freight. Their annual

shipments totaled $50$ million tons.

This year they are considering geographical expansion through the purchase of a smaller railroad

corporation that last year shipped a total of $30$ million tons. Economists estimated that the total

cost function $($for the merged corporations$)$ will be Y$=137+0\mathrm{.}1$T$,$ while $30\%$ more freight should

be expected due to the better geographic coverage, at a price discounted by $50$ cents.

a$)$ Which railroad realizes greater EOS? Use a numerical example or a graphic for proof.

b$)$ Calculate cost vs$.$ revenue to show numerically that the large railroad should merge with the

smaller one.