A Problem in Optimal Search and Stop

We are told that an object is hidden in one of m(m < ∞) boxes and we are given prior probabilities p_i⁰ that the object is in the ith box. A search of box i costs c_i and finds the object with probability α, if the object is in the box. Also, we suppose that a reward R_i is earned if the object is found in the ith box. A strategy is any rule for determining when to search, and, if so, which box. The major result is that an optimal strategy either searches a box with maximal value of α_ip_i/c_i or else it never searches such boxes. Also, if rewards are equal, then an optimal strategy either searches a box with maximal α_ipⁱ/c_i or else it stops.