The manager of a bakery is considering how many chocolate cakes to bake on any given day. The manager knows that the number of chocolate cakes that will be demanded by customers on any given day is a random variable whose probability density is given by

\(f(x)=\frac{x+1}{15} I_{\{0,1,2,3\}}(x)+\frac{7-x}{15} I_{\{4,5\}}(x)\).

The bakery makes a profit of \(\$ 1.50\) on each cake that is sold. If a cake is not sold on a given day, the cake is thrown away (because of lack of freshness), and the bakery loses \(\$ 1\). If the manager wants to maximize expected daily profit from the sale of chocolate cakes, how many cakes should be baked?