A doctor wants to schedule visits for two patients whohave been operated on for tumors

Chapter 15, Problem 37

(choose chapter or problem)

A doctor wants to schedule visits for two patients whohave been operated on for tumors so as to minimize theexpected delay in detecting a new tumor. Visits for patients1 and 2 are scheduled at intervals of x1 and x2weeks, respectively. A total of m visits per week is availablefor both patients combined.The recurrence rates for tumors for patients 1 and 2are judged to be v1 and v2 tumors per week, respectively.Thus, v1/(v1 + v2) and v2/(v1 + v2) are the probabilitiesthat patient 1 and patient 2, respectively, will havethe next tumor. It is known that the expected delay indetecting a tumor for a patient checked every x weeksis x/2. Hence, the expected detection delay for both patientscombined is given by10f(x1, x2) = v1v1 + v2x12 + v2v1 + v2x22 .Find the values of x1 and x2 in terms of v1 and v2 thatminimize f(x1, x2) subject to the fact that m, the numberof visits per week, is fixed.