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 $1,800 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 HomeGrowns lawyers charge $200 per hour, how long should the contract be?

I need the answer to be the exact number of years, rounded to 1 decimal point please.

Explanation / Answer

Let the number of years be Y

So total savings in bargaining = 1600Y

Legal fee for Y years=(Y^2)*150

Savings after legal fees=1600Y-150Y^2

For the above amount to be maximized , by differenciation , 2*150Y=1600 or Y=1600/300=5.33 years.

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