The flow on a $6-$lane freeway $($i$.$e$.,3$ lanes in each direction$)$ can be modeled using a $$truncated$$ Greenberg model. It is found that the jam density using the model is $115$ vehicles per lane per mile $($i$.$e$.,345$ vehicles per mile for $3$ lanes in one direction$).$ Also, as density decreases from the jam density, speed increases until some value k$$ such that at k$=22$ vehicles per lane per mile the speed is $75$ mph$.$ Then in the range $0<=$k$<=$k$\text{'},$ the speed is constant at $75$ mph$.$

Part a$.$ What is the total flow in vehicles$/$hour for $3$ lanes in one direction when k $=30$ vehicles per lane per mile?

Part b$.$ What is the total flow in vehicles$/$hour for $3$ lanes in one direction if k $=$ kmax, i$.$e$.,$ the density that maximizes flow?