so this is a somewhat simple question but im stumped, here's why:
given the utility U=2$X_1$+2$X_2$ where $P_1$$X_1$+$P_2$$X_2$=20 and $P_1$=0.5$P_2$
the question asks to find optimal values of $X_1$ and $X_2$, i tried using lagrangian method but the FOCs would only leave me with $\lambda$ and $P$ values. i also tried finding the MRS, which resulted in $1$, while the price ratio is $1:2$ , in both methods the quantities of goods 1 and 2 would disappear and I'd be trying to figure it out with what feels like incomplete information.
give it a try and tell me where i went wrong if possible.