PART  C : DECISION TREE
	EMV :- EXPECTED MONETARY VALUE
		or EXPECTED PAY OFF
	vvvvvv imP
	EX 1 FOR THE FOLLOWING  PAYOFF MATRIX FIND THE OPTIMAL DECISION USING DECISION TREE ( USE EMV METHOD)
	PAY OFF MATRIX
	Course of Action	State of Nature
	Alternative	S1	S2	S3
	A1	30	70	80
	A2	50	0	40
	A3	40	30	60
	Probability	0.3	0.5	0.2	1
		EXPECTED PAY OFF MATRIX
	Course of Action	State of Nature
	Alternative	S1	S2	S3	EMV
	A1	9	35	16	60
	A2	15	0	8	23
	A3	12	15	12	39
	EMV (A1) = 30*0.3+70*0.5+80*0.2 =9+35+16=60
	EMV (A2) = 50*0.3+0*0.5+40*0.2 = 15+0+8 = 23
	EMV (A3) = 40*0.3+30*0.5+ 60*0.2 = 12+15+12 =39
	OPTIMAL DECISION IS TO CHOOSE A1 BY EMV CRITERIA USING DECISION TREE
	EX 2	FIND THE BEST DECISION USING DECISION TREE BY EMV CRITERIA
			PAY OFF MATRIX
	Course of Action	State of Nature
	Alternative	S1	S2	S3	S4
	A1	35	100	38	75
	A2	58	95	105	55
	A3	45	30	91	100
	PROB	0.2	0.3	0.4	0.1
	SOLUTION
			EXPECTED PAY OFF TABLE
	Course of Action	State of Nature
	Alternative	S1	S2	S3	S4	EMV
	A1	7	30	15.2	7.5	59.7
	A2	11.6	28.5	42	5.5	87.6
	A3	9	9	36.4	10	64.4
	EMV (A1) = 35*0.2+ 100*0.3+ 38*0.2 =7+ 30+ 15.2+ 7.5 = 59.7
	EMV (A2) =  11.6 + 28.5 + 42 +5.5 = 87.5
	EMV (A3) = 9 + 9 +36.4 + 10 + 64.4
	BEST DECISION IS TO SELECT A2 BY EMV CRITERIA USING DECISION TREE
	Ex 3 :  FIND THE BEST DECISION USING EMV CRITERION
		PAY OFF MATRIX
	EVENTS	A1	A2	A3	PROB
	E1	25	-125	-10	0.5
	E2	400	400	440	0.4
	E3	650	750	740	0.1
		PAY OFF MATRIX
			EVENTS
	ALTERNATIVES	E1	E2	E3
	A1	25	400	650
	A2	-125	400	750
	A3	-10	440	740
	PROB	0.5	0.4	0.1
			EXPECTED PAY OFF TABLE
	EVENTS	E1	E2	E3	EMV
	A1	12.5	160	65	237.5
	A2	-62.5	160	75	172.5
	A3	-5	176	74	245
	EMV (A1) = 12.5 + 160 + 65 = 237.5
	EMV (A2) =  -62.5+ 160 + 75 = 172.5
	EMV (A3) = -5 +176 +74 = 245
	BEST DECISION IS TO SELECT A3 BY EMV CRITERIA USING DECISION TREE