2. (20 marks) A contractor would like to purchase a truck to replace an old one. There are three models available Carrying capacity ('000 kg) 25 30 35 Price ('000 $) 120 140 155 Most current jobs require a carrying capacity of 25,000 kg only. However, a higher carrying capacity might be needed in the future. The truck dealer suggested that it is possible to add an upgrade kit in the future but cannot promise a price. The following are possible cost of the upgrade kits Upgrade Kits Possible Price ('000 $) Probability 19 23 27 32 39 41 13 19 21 0.20 0.50 0.30 0.25 0.55 0.20 0.30 0.50 0.20 Converting 25,000 kg to 30,000 kg Converting 25,000 kg to 35,000 kg Converting 30,000 kg to 35,000 kg The contractor has to decide whether it is better to purchase a truck of bigger capacity now or purchase a smaller truck now and order an upgrade kit only if needs arise. Here are the probability of the potential carrying capacity needs in the future: Potential carrying capacity needs ('000kg)Probability 25 30 35 0.3 0.3 0.4 Please use decision tree to help the contractor to decide what is the most cost-effective purchasing option (note: all prices are present worth; no need to consider interest rate) 2. (20 marks) A contractor would like to purchase a truck to replace an old one. There are three models available Carrying capacity ('000 kg) 25 30 35 Price ('000 $) 120 140 155 Most current jobs require a carrying capacity of 25,000 kg only. However, a higher carrying capacity might be needed in the future. The truck dealer suggested that it is possible to add an upgrade kit in the future but cannot promise a price. The following are possible cost of the upgrade kits Upgrade Kits Possible Price ('000 $) Probability 19 23 27 32 39 41 13 19 21 0.20 0.50 0.30 0.25 0.55 0.20 0.30 0.50 0.20 Converting 25,000 kg to 30,000 kg Converting 25,000 kg to 35,000 kg Converting 30,000 kg to 35,000 kg The contractor has to decide whether it is better to purchase a truck of bigger capacity now or purchase a smaller truck now and order an upgrade kit only if needs arise. Here are the probability of the potential carrying capacity needs in the future: Potential carrying capacity needs ('000kg)Probability 25 30 35 0.3 0.3 0.4 Please use decision tree to help the contractor to decide what is the most cost-effective purchasing option (note: all prices are present worth; no need to consider interest rate)