Consider the cost information given in Exercise $10\mathrm{.}20.$ Suppose that the process model represented by equation $10\mathrm{.}31$ is appropriate. It requires $2$ h to investigate a false alarm, the profit per hour of operating in the in$-$control state is $$500,$ and it costs $$25$ to eliminate the assignable cause. Evaluate the cost of the arbitrary control chart design n$=5,$ k $=3,$ and h $=1.$