ian is looking to invest up to 40000$ in 5 different investment opportunities. Data on is given below. he wants to make sure that the fraction invested in industrial opportunities is no more than 0.6, and that the weighted average ( with the amount invested as the weights) maturity of the investment is no more than 14 years. assume money can not be invested in the same opportunity twice. formulate the problem of determining how much to invest in each opportunity in order to maximize the total return from all the investments subject to the constraints stated above. also, formulate the problem of detemining how much to invest in each opportunity in order to maximize the average annual return.

opportunities	annual return	maturity
A: government bonds	6%	10years
B: government bonds	5%	5years
C: prefered shares(industry)	7%	20years
D: Bonds(industry)	4%	6years
E: CDs	5.5%	7years