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 $1,300 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 $160 per hour, how long should the contract be?

Explanation / Answer

L= Y2

AS its quadratic relationship

number of hours of lawyer = (number of years of contract)^2

Contract duration will be till the point where savings are higher or equal to costs incurred

$1300* number of years >= $160 *(number of years)^2

use hit and trial method, we estimate 8 hours

at 8 hours

total savings will be = $1300*8 = $10,400

Total costs will be = $160* (8)^2 = $160*64 = $10,240

if we have used 9 hours, costs will be higher than savings, so

the answer is 8 hours

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