A rectangular footing with a rough base is to be constructed as below figure. a$.$ With the given soil profile, determine the ultimate bearing capacity $($bearing capacity at failure$)$ using a generalized bearing capacity equation. Assume bearing capacity will be controlled by top sand layer.b$.$ Determine the allowable bearing capacity $($allowable bearing pressure$)$ when factor of safety equals $3.$c$.$ Calculate the elastic compression settlement in the sublayer $1$ at allowable bearing pressure right after construction $($t $=1)$ and $50$ years after the construction $($t $=50),$ using Schmertmanns method. Assume $(==15000$ MPa in sublayer $1.$d$.$ Calculate the primary consolidation settlement in the sublayer $2$ at allowable bearing pressure.