Elasticity of A+XI[X] domains where A is a Dedekind domain

Let A be a Dedekind domain and I be an ideal of A. We investigate the elasticity of integral domains of the form R=A+XI[X]. Namely, when the ideal class group of A is infinite, we show that the elasticity of R is infinite, and when this group is finite, we bound from below and above the elasticity of R using the number of prime ideals in the factorization of I and some Davenport-type constants. We derive the exact value of the elasticity in some special cases.