Question

uestion 3 10 points Save Answ. A concessionaire for the local ballpark has developed a table of conditional values for the various alternatives (stocking decision) and states of nature (size of crowd). 9 Probability Alternative 1 Alternative 2 Alternative 3 Large 3 .000 22,000 1 5,000 Average 15 12,000 5,000 12,000 Small 12 2,000 6,000 5,000 If the probabilities associated with the states of nature are 0.30 for a large crowd, 0.50 for an average crowd, and 0.20 for a small crowd, determine: (a) the opportunity loss table. (b) minimum expected opportunity loss (EOL).

Answer 1

We are to subtract each of values in column of Si( i=1,2,3) from largest payoff in the same column.

Opportunity loss Table( Regret Table)

States of nature Probability	S¹ Large 0•3	S² Average 0•5	S³ Small 0•2
Alternatives
A¹	13000 ( 22000-9000)	0 120000-120000)	8000 (6000-(-2000)
A²	0 (22000-22000)	6000 (12000-6000)	0 (6000-6000)
A³	7000 (22000-15000)	0 (12000-12000)	1000 (6000-5000)

b) Expected Oppotunity loss ( EOL) of alternatives A¹,A²,A³ are as follows------

A¹= 13000×0•3+0×0•5+8000×0•2

3900+0+1600= 5500

A²=0×0•3+6000×0•5+0×0•2

0+3000+0=3000

A³=7000×0•3+0×0•5+1000×0•2

2100+0+200=2300

As ,we observe, in case of Alternative 3(A³), EOL is minimum.