(a) Describe what do you mean by the time-optimal control problem. Give an example of a time optimal control problem. [4 Marks] (b) Four doctors to be allocated optimally in three different hospitals. Table 1 shows the number of patients the doctors can serve per hour. Use dynamic programming to Table 1: Patients L(a) served in i-th hospital Doctors (r) Lo(r) L(x) L(x) 1 4 2 5 2 6 4 7 3 9 7 8 10 11 determine the allocation of doctors in order to serve the maximum number of patients. [12 Marks]