Really need help with this linear optimization problem,
A bank has $2 million in new funds that must be allocated to home loans, personal loans, and automobile loans. The annual rates of return for the three types of loans are 8% for home loans, 15% for personal loans, 10% for automobile loans. The bank’s planning committee has decided that at least 40% of the new funds must be allocated to home loans. In addition, the planning committee has specified that the amount allocated to personal loans cannot exceed 60% of the amount allocated to automobile loans.
Formulate a linear model that can be used to determine the amount of funds the bank should allocate to each type of loan to maximize the total annual return for the new funds. Run solver to generate the optimal solution.