$$S = \{ \alpha \in \mathbf{R}^3 \mid \alpha_1 + \alpha_2e^{-t} + \alpha_3 e^{-2t} \leq 1.1 \mbox{ for } t\geq 1\}$$
Is $S$ affine, and is it a polyhedron?
I thought it's basically a linear function in $\alpha$, thus affine. Since the linear function is characterized by $t$, as $t$ changes, there are many linear functions, thus a polyhedron? Is my reasoning correct, please?
Supplement:
Plotted @A.Γ's equation
