Arlington and Belmont are two adjacent towns in Massachusetts. Each town is preparing for the coming winter season by purchasing salt for its roads. A supplier has offered salt at $2 per ton and each town must make a commitment in September for the total amount to be supplied. Assume any salt left over deteriorates and cannot be used for the following season. Based on historical records of the amount of snowfall and road salting required, the amount of salt needed in Arlington for the coming season has a normal distribution with a mean of 10,000 tons and standard deviation of 3000 tons. The amount of salt needed in Belmont for the coming season also has a normal distribution with the same mean of 10,000 tons and the same standard deviation of 3000 tons. If during the season a town runs out of salt, unlimited additional amounts can be purchased on the spot market for immediate delivery at a price of $15 per ton. The political consequences of not salting the roads are extreme and a town would never choose not to buy the needed salt. Assume that Arlington and Belmont act independently, and sign separate contracts with the supplier

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To determine how much salt each town should order we can calculate the amount of salt needed to meet ... View the full answer