Paul and Anna have a home cleanliness of quality u(x, y). Anna contributes x hours daily to household chores and Paul contributes y hours daily. The number of hours that each person actually dedicates to chores daily depends on how heavy traffic is (t), and how much time Paul spends daily doing Anna's baking (b). This can be shown as x = f(t, b) and y = g(t, b). 

What is the likely effect of b on the quality of the home cleanliness? Justify mathematically. 

Suppose the traffic level is t = 10. How do you find the value of b so that the maxmium home cleanliness quality is achieved? Show all steps.