IBM must determine whether to mount a small or large advertising campaign during the coming year. IBM believes there is a 1/4 probability that its rival, HP, will mount a small ad campaign, and a 3/4 probability that HP will mount a large ad campaign. At the end of the current year, IBMs market share and profits (in millions of dollars) will be as follows:

If both HP and IBM choose small ad campaigns, then IBM will have a 50% market share and a profit of $20 million dollars.

If both HP and IBM choose large ad campaigns, then IBM will have a 35% market share and a profit of $15 million dollars.

If HP chooses a small ad campaign and IBM chooses a large ad campaign, then IBM will have a 55% market share and a profit of $12 million dollars.

If HP chooses a large ad campaign and IBM chooses a small ad campaign, then IBM will have a 50% market share and a profit of $10 million dollars.

IBM has a utility function of

U(x,y) =.8 U_X(x) + .4 U_Y(y)- 0.2 U_X(x) U_Y(y), where:

x is market share (in %); U_X(x)= (x/20)^1/2, and

y is profit (in millions of dollars); U_Y(y)= ln(y)

Draw a decision tree, and find the strategy that maximizes IBMs expected utility.