Solve exp question

I have a problem:

min : y/x * (exp(x) + C)

s.t. sum(y) <= A
sum(x) <= B

where C is a constant. x and y are variables of length N.
By replacing z = y/x, the original problem can changed be an exponential cone.z * (exp(y/z) + C),

{y,z,ZZ} = expnential{1};

min ZZ + z * C

but the constraints are not affine which will break the DCP rule set.

Any hint on how to reformulate the problem?

Can you demonstrate convexity? I don’t see it. If not, then the answer is no: no amount of reformulation will make this work with CVX.