How do you find marginal revenue if you don't have a production function? I was given a word problem. No formulas. So I set up the following equations: 

Demand Function 
\begin{equation}
D(p) = a - p
\end{equation} 
Cost Function: 
\begin{equation}
c(q) = 9 + 10q
\end{equation} 
Marginal Cost 
\begin{equation}
MC = 10
\end{equation} 

I am supposed to find how much the man in the problem would produce for any value of $a$. But, without a production function, I am unsure how to determine how much he will produce. 

Specifically, suppose I write 

\begin{equation}
R = pD(p) 
\end{equation}  

I can't then differentiate R by q to find marginal revenue. 

So how do I know how much he would produce?
Here are some hints. Either solve the profit function in terms of $p$, substituting out all references to $q$ (recall that $D(p) = q$), or solve the profit function in terms of $q$, substituting out all references to $p$. Then you'll find that the profit function is concave and the differentiated with respect to $p$ in the first case or $q$ in the second case will give you the profit maximizing solution.

EDIT: Yeah, $a = 2q + 10$ looks correct. Just solve the equation for $q$ and the interpretation is clear. That is, the quantity produced is $q = (a - 10)/2$. If you want to know the price, then just substitute $q$ in for $D(p)$ like so: $a - p = D(p) = q = (a - 10)/2$.