Assignment:
A bank has set aside a maximum of $25 million for commercial and home loans. Every million dollars in commercial loans requires 2 lengthy application forms, while every million dollars in home loans requires 3 lengthy application forms. The bank cannot process more than 72 application forms at this time. The bank's policy is to loan at least four times as much for home loans as for commercial loans. Because of prior commitments, at least $10 million will be used for these two types of loans. The bank earns 10% on commercial loans and 12% on home loans. What amount of money should be allotted for each type of loan to maximize the interest income?
Please show all formulas using the simplex method and the associated table for each simplex tableau.
Provide complete and step by step solution for the question and show calculations and use formulas.