Dantzigbank is attempting to determine where its assets should be invested durin
ID: 3172932 • Letter: D
Question
Dantzigbank is attempting to determine where its assets should be invested during the current year. At present, $500,000 is available for investment in bonds, home loans, auto loans, and personal loans. The annual rate of return on each type of investment is known to be To ensure that its portfolio is not too risky, Dantzigbank's investment manager has placed the following three restrictions on the bank's portfolio: The amount invested in personal loans cannot exceed the amount invested in bonds. The amount invested in home loans cannot exceed the amount invested in auto loans. No more than 25% of the total amount invested may be in personal loans. The bank's objective is to maximize the annual return on its investment portfolio. Formulate a linear program that will enable Dantzigbank to meet this goal. Solve the LP using Matlab (linprog). Provide the optimal solution; the optimal objective value; and the matlab script used to solve the problem.Explanation / Answer
Let amount invested in bonds, home loans, auto loans and personal loans be B,H,A and P respectively.
We want to maximize returns :
Max Z = 0.1*B + 0.16*H + 0.13*A + 0.20*P
subject to Constraints:
1. P<=B
2. H<=A
3. P<=0.25*500000
4. P + B + H + A = 500000
Optimal solution:
B=H=A=P=125000
Optimal objective value i.e. annual return = 73750
Script:
f = -1*[0.1;0.16;0.13;0.20];
A = [-1,0,0,1;
0,1,-1,0;
0,0,0,1];
b = [0;0;125000];
Aeq = [1,1,1,1];
beq = [500000];
x = linprog(f,A,b,Aeq,beq);
-f'*x
x
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