Peanut Company recently acquired a peanut$-$processing company that has a normal annual capacity of $3,000,000$ pounds and that sold $2,700,000$ pounds last year at a price of $$2\mathrm{.}00$ per pound. The purpose of the acquisition is to furnish peanuts for the peanut butter plant, which needs $700,000$ pounds of peanuts per year. It has been purchasing peanuts from suppliers at the market price. Production costs per pound of the peanut$-$processing company are as follows:

Direct materials $$0\mathrm{.}50$

Direct labor $0\mathrm{.}26$

Variable overhead $0\mathrm{.}11$

Fixed overhead at normal capacity $0\mathrm{.}21$

Total $$1\mathrm{.}08$

Management is trying to decide what transfer price to use for sales from the newly acquired Peanut Division to the Peanut Butter Division. The manager of the Peanut Division argues that $$2\mathrm{.}00,$ the market price, is appropriate. The manager of the Peanut Butter Division argues that the cost price of $$1\mathrm{.}08($or perhaps even less$)$ should be used since fixed overhead costs should be recomputed. Any output of the Peanut Division up to $2,700,000$ pounds that is not sold to the Peanut Butter Division could be sold to regular customers at $$2\mathrm{.}00$ per pound.

$($a$)$ Compute the annual gross profit for the Peanut Division using a transfer price of $$2\mathrm{.}00.$