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

Investment               Rate of return

Bonds                             10%

Home loans                      16%

Auto loans                       13%

Personal loans                  20%

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

Part 1: Formulate a linear program that will enable Dantzigbank to meet this goal.

Part 2: Solve the LP using Matlab (linprog). Provide

i) the optimal solution;

ii) the optimal objective value; and

iii) the matlab script used to solve the problem.