$($Prepared from a situation suggested by Professor John W$.$ Hardy.$)$ Lone Star Meat Packers is a major processor of beef and other meat products. The company has a large amount of T$-$bone steak on hand, and it is trying to decide whether to sell the T$-$bone steaks as they are initially cut or to process them further into filet mignon and the New York cut.

If the T$-$bone steaks are sold as initially cut, the company figures that a $1-$pound T$-$bone steak would yield the following profit:

Selling price $($$$2\mathrm{.}20$ per pound$)$ $ $2\mathrm{.}20$

Less joint costs incurred up to the split$-$off point where T$-$bone steak can be identified as a separate product $1\mathrm{.}35$

Profit per pound $ $0\mathrm{.}85$

If the company were to further process the T$-$bone steaks, then cutting one side of a T$-$bone steak provides the filet mignon and cutting the other side provides the New York cut. One $16-$ounce T$-$bone steak cut in this way will yield one $6-$ounce filet mignon and one $8-$ounce New York cut; the remaining ounces are waste. It costs $$0\mathrm{.}15$ to further process one T$-$bone steak into the filet mignon and New York cuts. The filet mignon can be sold for $$4\mathrm{.}00$ per pound, and the New York cut can be sold for $$3\mathrm{.}70$ per pound.

Required:

$1.$ What is the financial advantage $($disadvantage$)$ of further processing one T$-$bone steak into filet mignon and New York cut steaks?

$2.$ Would you recommend that the T$-$bone steaks be sold as initially cut or processed further?