1. A gas company can either buy its supply this year at a cost of $600,000 or spend $1,000,000 to drill for natural gas. If it hits a gusher (20% chance) the company will bring in $2,700,000 of revenue, but if the deposit is moderate (30% chance) it will bring in $1,400,000. in either case, they will In either case, they will have enough supply. If the well comes up dry, then the company will have to buy it's supply at new market price. For the new market, there is 20% chance the price will stay the same, a 10% chance it will drop by 5%, a 20% chance it will be 5% higher, a 25% chance it will be 10% higher, and otherwise it will be 15% over the current price. If the company buys it supply, then he believes that a revenue of $900,000 will be produced. Construct a decision tree for the situation and determine the best strategy.
2. A gambler has an opportunity to play the following two-stage game. Initially the gambler must pay $5 and must choose between a white box and a black box. The white box contains 5 blue cards, 4 green cards, and 6 purple cards. The black box contains 3 blue cards, 5 Green cards, and 12 purple cards. The cards are all identical except for color. If a green card is drawn, the player has lost and game is over. If a purple card is drawn, The house pays $15. If a blue card is drawn, the player may now quit or move on to stage two for an additional cost of $10. In stage 2 the player draws a card at random from a box that contains 3 yellow and 7 orange cards. If in stage 2 the player draws and orange card, the house pays $35. If a yellow card is selected, the house pays $0z. construct a decision tree and determine the best strategy based on maximizing expecting payoff.
3. An investor could invest his money in one of three different investment plans over an 18 month period. The return on his investment depends on the type of investment plan chosen and the future state of the economy. The three plans consists of buying convertible bonds, purchasing government bonds, or investing in money market funds. In particular, He can buy convertible bonds for $10,000, invest $8000 in the money market funds, or by $15,000 worth of government bonds. The economy has been forecasted to be gloomy was a probability of .30, stable with the probability of .45, or rosy with a probability of .25. The total amount collected, including the initial investment, for the government bonds is $16,000 for a rosy economy, $15,900 for a stable economy, and $14,500 for a gloomy economy. The amount collected for the money market funds investment is $9000 for rosy, $8900 for stable economies. However, when the economy is gloomy, the investor can pay a fee of $350 and sell his money market funds prematurely in which case he collects $8900. Otherwise, he may wish to do nothing and collect $8700. The convertible bonds investment will result in collecting $11,000 in a rose economy. Understand look on me, the investor can sell the convertible bonds prior to maturity for a fee of $200 and collect $11,100, or wait till the end of the 18 months and collected thousand $500. When the economy is gloomy,he can sell the convertible bonds prematurely and invest in real estate bonds at a cost of $500 in which case he will collect $10,500, or he can do nothing it's like $9800. Construct a decision tree that represents investment plans and determine the optimal investment plan which will maximize his expected profit investor who missing money he can sell the convertible bonds prematurely and invest in real estate bonds at a cost of $500 in which case he will collect $10,500, or he can do nothing it's like $9800. Construct a decision tree that represents investment plans and determine the optimal investment plan which will maximize his expected profit.