You need to buy a new cell phone now and are trying to minimize your cell phone costs for the next 5 years. A new cell phone costs C dollars and lasts for at most 3 years. The estimated maintenance cost for a phone depends on its age; if a phone is in its ith year of life, the cost will be M_i dollars, i = 1, 2, 3. Assuming cell phones have no salvage value and that you have the option each year of buying a new phone (for C dollars), formulate a network model that will minimize your costs over the next 5 years.

The management of a supermarket wants to adopt a new promotional policy of giving a free gift to every customer who spends more than a certain amount per visit at this supermarket. the expectation of the management is that after this promotional policy is advertised, the expenditures for all customers at this supermarket will be normally distributed with a mean of $95 and a standard deviation of $20. if the management wants to give free gifts to at most 10% of the customers, what should the amount be above which a customer would receive a free gift?