What is the optimization problem for Financial institution? And what is its first order condition? (The picstures are the lecture note)

Financial intermediaries and monetary authority Financial intermediaries behave competi- tively. They receive Dt in deposits from households and Xt on households's be half from the central bank. The representative financial intermediary receives deposits from households and cash from the mon- etary authority. It then lends out loan to firms. In the end of the period, the intermediary pays Rt Dt to households for their deposits, and distribute RtXt to households in the form of profits. It maximizes its cash flow given by: (9) subject to (10) Lt Financial intermediaries and monetary authority Financial intermediaries behave competi- tively. They receive Dt in deposits from households and Xt on households's be half from the central bank. The representative financial intermediary receives deposits from households and cash from the mon- etary authority. It then lends out loan to firms. In the end of the period, the intermediary pays Rt Dt to households for their deposits, and distribute RtXt to households in the form of profits. It maximizes its cash flow given by: (9) subject to (10) Lt