Linear/ Non linear Programming

Maximize the annual return R(t) of a portfolio with S(t) being the initial investment. The market value is a function of time and can change randomly. By using call option c(t) contract \& put option p(t) contract, you can eliminate any downturn of your portfolio value and / or enhance the return of your portfolio, if selected properly. MaximizeR(t)=S(t)+n1p(t)+n2c(t) such that n1+n2=N unit cost per: S(t)=T($1M)p(t)=S(t)/12c(t)=S(t)/10