Investment manager Max Gaines has several clients who wish to own a mutual fund portfolio that matches,as a whole,the performance of the S&P 500 stock index.His task is to determine what proportion of the portfolio should be invested in each of the five mutual funds listed below so that the portfolio most closely mimics the performance of the S&P 500 index.Formulate the appropriate nonlinear program. 
Definitions:
Government Assistance
Programs or financial aid provided by the government to individuals, businesses, or other entities in need of support.
Deferred Gratification
The ability to resist the temptation for an immediate reward and wait for a later reward.
Paycheque
A paycheque is a check issued by an employer to pay an employee for services rendered, typically on a regular basis like weekly or monthly.
Savings Account
A deposit account held at a bank or other financial institution that provides modest interest rates.
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