Section A
Q1.
(a) subject to 3x1 + 4x2 ≤ 6 x1 + 3x2 ≥ 2 x1, x2 ≥ 0 using Simplex procedure.
(i) Describe dynamic programming problem and discuss its applications.
(b) (ii) State Bellman's optimality criteria. (iii) Minimize Z = y12 + y22 + y32 subject to y1 + y2 + y3 ≥ 18 y1, y2, y3 ≥ 0 For two players A and B, the payoff matrix is given below :
(c) Player B B2 B3 B4 B\rm 5 B1 3 \overline4 8 4 \mathbf2 A1 (A2)/(A3) 6 \boldsymbol7 5 3 8 Player A 8 б \overline7 9 7 3 4 2 8 4 A4 Using dominance property, find the value of the game and optimal strategies of the players. Check whether strategies adopted by player A are mixed or pure. There are three dentists in a dental clinic. On an average, it takes minutes
(d) on one patient and service times follow exponential distribution. Patients arrive according to Poisson process with mean 6/hour and queue discipline followed is FIFO (FCFS). Calculate the following:
(i) Expected number of patients in the queue (ii) Expected amount of time spent by a patient in the clinic (iii) Percentage of idle time of any dentist (iv) Probability that all dentists are busy 10 2 DFSE-F-STT/6
