HomeGrown is a small restaurant that specializes in serving local fruits, vegeta

Question

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 $1,400 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 $140 per hour, how long should the contract be?

Explanation / Answer

The quadratic relationship is L=Y2 , cost of lawyer is 140L=140 Y2 , savings per year is 1400Y. Thus we get the equation as 140 Y2-1400Y=0. Thus solving it further we get Y=10. Thus the number of years for the contract should be 10 years.

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