Question $2$

A farmer sells cocoa for $1\mathrm{.}48$ dollars per kilogram. It costs the farmer $0\mathrm{.}47$ dollars to produce one kilogram. The farmer has fixed costs of $206$ dollars.

a$.$ Find the total cost function $C(q),$ where q is the number of kilograms of cocoa produced.

b$.$ Find the revenue function $R(q),$ where q is the number of kilograms of cocoa sold.

c$.$ Find the profit function $P(q).$

d$.$ What is the marginal profit? Include units.

Please show work step by step