Question

3. JApplication of Linear Programming in Finance - Model Formulation (10 pts)] Jacksonville Trust Co. LTD invests in various types of securities. They have $12 million for immediate investment and wish to maximize the interest earned over the next year. Risk is not a uctor. Preferred investment alternatives include Bonds (B), Stocks (S), Gold (G), Land (L), BitCoin* (C), and famous Art Masterpieces (M). The expected return for Bonds is 5%, Stocks 12%, Gold 11%, Land 4%, BitCoin 2%, and Art Masterpiece 3%. The maximum amount to be invested for each alternative is $2 million for Bonds, $1 million for Stocks, $2 million for Gold, $1 million for Land, $2 million for BitCoin, and $3 million for Art Masterpiece. To structure the portfolio, the Senior VP has specified that at least 20% of the investment should be in corporate Bonds, common Stocks, and BitCoin; and no more than 35% of the investment is to be in Gold and Land. In addition, the total investments on Bond, Stocks, and Gold should be greater than the total amount of money invested on Land, BitCoin, and Art Masterpiece. The objective is to maximize the retum. Formulate a linear model for financial portfolio optimization. *BitCoin: an innovative consensus payment network that enables a new payment system and a completely digital money. (You don't have to solve this problem using either EXCEL Solver or QM for Windows.) (a) What are the Decision Variables? (1 pt) (b) What is the Objective Function? (2 pts) (c) What are Constraint Equations including non-negativity constraints? (pts)

Answer 1

(a) Decision variables are B, S, G, L, C, and M which represent the amount (in $ millions) to be invested in each of the investment alternatives: Bonds (B), Stocks (S), Gold (G), Land (L), BitCoin* (C), and famous Art Masterpieces (M)

(b) Objective function is Maximization of expected return. So Objective is Max 0.05B + 0.12S + 0.11G + 0.04L + 0.02C + 0.03M

(c) Constraint equations are following

B + S + G + L + C + M <= 11

B <= 2

S <= 1

G <= 2

L <= 1

C <= 2

M <= 3

B + S + C >= 0.2*(B + S + G + L + C + M)

G + L <= 0.35*(B + S + G + L + C + M)

B + S + G >= L + C + M

B, S, G, L, C, M >= 0

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