The Speculators Fund is a stock mutual fund investing in categories j = 1,c, n of common stocks. At least a fraction /j and at most fraction uj of the fund’s capital is invested in any category j. The fund maintains estimates, vj, of the expected annual return in capital gain and dividends for each dollar invested in category j.

They also estimate the risk, rj, per dollar invested in each category j. The goal is to maximize return at minimum risk.

(a) Explain why appropriate decision variables for a model of this problem are xj ! fraction of fund capital invested in category j

(b) Formulate an objective function maximizing expected return per dollar invested.

(c) Formulate an objective function minimizing risk per dollar invested assuming that risks for different categories are independent of one another.

(d) Formulate a main constraint assuring that 100% of the fund’s capital is invested somewhere.

(e) Formulate a system of n constraints enforcing lower bounds on the fraction of fund capital invested in each category.

(f) Formulate a system of n constraints enforcing upper bounds on the fraction of fund capital invested in each category.

(g) Is your model best classified as an LP, an NLP, an ILP, or an INLP, and is it singleor multiobjective? Explain.