Home-Grown is a small restaurant that specializes in serving local fruits, vegetables, and meats. The company has chosen to enter into a long-term relationship with Family Farms, a local farming operation. The two parties have decided to enter into a long-term contract, where Family Farms will supply produce to Home-Grown at specified prices and volume each year. Before signing a contract, Home-Grown is trying to decide how long the contract should be. It estimates that each year the contract covers saves the restaurant $1,000 in bargaining and opportunism costs. However, each year the contract covers also requires more legal fees. Home-Grown estimates that the number of hours required from lawyers, L, has a quadratic relationship with the number of years on the contract, so that L = Y2, where Y is the number of years for the contract. If Home-Grown’s lawyers charge $100 per hour, how long should the contract be?
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