Part II. Problem Solving (50 points) 1. [Linear Programming-Model Formulation (1
ID: 375242 • Letter: P
Question
Part II. Problem Solving (50 points) 1. [Linear Programming-Model Formulation (10 pts)] Jacksonville Trust Co. LTD invests in various types of securities. They have $9 million for immediate investment and wish to maximize the interest earned over the next year. Risk is not a factor. Preferred investment alternatives include Bonds (B), Stocks (S), Gold (G), Land (I), BitCoin (C), and famous Art Masterpieces (M). The expected return for Bonds is 5%, Stocks 12%, Gold 1 1%, Land 4%, BitCoin 2%, and Art Masterpiece 39. 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% ofthe investment should be in corporate Bonds, common stocks, and Bidon; 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 return. Formulate a linear model "BitCoin: an innovative consensus payment network that enables a new payment system and a completely digital money (a) What are the Decision Variables? (2 pts) b) What is the Objective Function? (3 pts) (c) What are Constraint Equations including non-negativity constraints?(5 pts)Explanation / Answer
The objective is to maximize the return yielding the following linear programming model
B=Dollars to invest in Bonds over the next year
S= Dollars to invest in Stock over the next year
G= Dollars to invest in Gold over the next year
L= Dollars to invest in Land over the next year
C= Dollars to invest in BitCoin over the next year
M= Dollars to invest in Art Masterpiece over the next year
Objective function is:-
Maximize Z = 0.05+0.12S+0.11G+0.04L+0.02C+0.03M
Subject to:-
B+S+G+L+C+M<9,000,000
B<2,000,000
S<1,000,000
G<2,000,000
L<1,000,000
C<2,000,000
M<3,000,000
B+S+C>0.2(B+S+G+L+C+M) OR 0.8B+0.8S-0.2G-0.2L+0.8C-0.2M>0
G+L<0.35(B+S+G+L+C+M) OR -0.35B-0.35S+0.65G+0.65L-0.35C-0.35M<0
B+S+G>L+C+M OR B+S+G-L-C-M>0
B,S,G,L,C,M0