Adam is indulging in his second favourite pastime of planning when he should refuel his car. The amount of fuel he uses in a week depends on traffic, how much driving he does during the week, and his driving style. From past experience Adam expects there is a 0.1 probability of no fuel use, 0.3 probablility of 1/4 tank of fuel use, 0.4 probablility of 1/2 tank of fuel use, and 0.2 probability of 3/4 tank of fuel use. He also estimates at the start of a week it will cost him $20 to fill his tank by a 1/4 of a tank of fuel, $40 to fill his tank by 1/2 tank, $60 to fill his tank by 3/4 of a tank and $80 to fill an empty tank to full. Note if Adam runs out of fuel it costs him an emergency call-out fee of $40 in addition to the cost of refueling to a full tank. Adam has determine the folllowing refuelling strategies - Refuel his car when it runs out of fuel; - Refuel his car when it the tank is 1/4 full; - Refuel his car when it the tank is 1/2 full; and - Refuel his car when it the tank is 3/4 full. Note Adam intends to refuel his car to a full tank when he does refuel his car. Help Adam determine which refuelling strategy is best to refuel his car so as to minimise the refuelling cost per week. To help in your calculations you should determine the average time between refuelling. Hint: You will need to include absorbing states in your formulation