HomeGrown 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 HomeGrown at specified prices and volume each year.Before signing a contract, HomeGrown 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.HomeGrown estimates that the number of hours it will need 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 HomeGrown's lawyers charge $100 per hour, how long should the contract be?

years