Maximizing function over a line

Question

Let

$$J(x,y) := x - h(y)$$

where $h : \Bbb R \to \Bbb R$ and $h''(x) > 0$ for each $x$. For $p, q > 0$ and $c \in \Bbb R$ the problem is:

$$\begin{array}{ll} \text{maximize} & J(x,y)\\ \text{subject to} & p x + q y = c\end{array}$$

1. What is the value of Lagrange multiplier?

2. Find the solution $(x,y)$ as function of $p$ and $q$?

Thanks!