Even though independent gasoline stations have been having a difficult time, lan Langella has been thinking about starting his own independent gasoline station. lan's problem is to decide how large his station should be. The annual returns will depend on both the size of his station and a number of marketing factors related to the oil industry and demand for gasoline. After a careful analysis, lan developed the following table: Figure 1 Size of First Station States of Nature Good Fair Poor Market Market Market Small $40,000 $18,000 -$8,000 Medium Large Very Large $90,000 $27,000 -$22,000 $105,000 $27,500 - $38,000 $320,000 $28,000 - $180,000 For example, if lan constructs a small station and the market is good, he will realize a profit of $40,000. This exercise contains only part e. e) The correct decision tree for lan, if each outcome is equally likely, is presented in G (1/3) $40,000 F (1/3) $18,000 P (1/3) $16,667 -- $8,000 Small G (1/3) -$90,000 Medium F (1/3) -$27,000 P (1/3) $31,667 -$22,000 Large G (1/3) $105,000 F (1/3) -$27,500 P (1/3) $16,667 $32,167 -- $36,000 G (1/3) $55,333 -$320,000 Very Large F (1/3) -$26,000 P (1/3) G = Good, F = Fair, P = Poor - $180,000 Q Figure 2 G(1/3) $40,000 F(1/3) $18,000 G P(1/3) $16,667 -$8,000 Small G(1/3) *$90,000 F(1/3) Medium -$27,000 P(1/3) $31,667 - $22,000 G (1/3) Large -$105,000 F(1/3) $27,500 P(1/3) $55,333 $32,167 - $36,000 G(1/3) $55,333 Very Large F(1/3) $320,000 $26,000 P (1/3) G=Good, F = Fair, P = Poor - $180,000 Q Figure 3 G(1/3) $40,000 F (1/3) $18,000 G P(1/3) $40,000 --$8,000 Small G(1/3) $90,000 F(1/3) Medium -$27,000 P(1/3) $90,000 - $22,000 Large G (1/3) $105,000 F(13) P(1/3) $27,500 $320,000 $105,000 - $36,000 G(1/3) $320,000 $320,000 Very Large F(1/3) -$26,000 P(1/3) G= Good, F = Fair, P = Poor - $180,000