This problem is quite specific and will help me to study for an
upcoming exam. (Complete solutions will be greatly appreciated!)

"Suppose there are 2 industries for goods X and Y, with technologies
represented by X=min{2l,k} and Y=l+k, where l and k are the two
factors of production. Suppose there is one consumer with preferences
represented by u(x,y)=x^(1/3)y^(2/3) who supplies the inputs
(perfectly-)inelastically and has an endowment of (l,k)=(8,24). What
is the competitive equilibrium for this economy?"