A family in Hong Kong requires 6 million dollars to finance a new home, and three different banks have agreed to supply all or part of this amount. Although each bank insists that the loan plus interest charges be repaid over 6 years, the repayment schedules differ from bank to bank, as shown in the following table. Bank 1 Bank 2 Bank 3 Percent of principal to be repaid each year Year 2 Year 3 Year 4 Year 5 Year 1 0 5 40 0 15 40 30 25 0 40 35 35 50 40 15 Year 6 55 45 15 The family feels that it is advantageous to borrow in such a manner that the total yearly payments on the loan are as nearly as equal as possible, yet it does not wish to pay more than 4 million dollars in total interest charge. Set up a linear programming model that will determine the amount of money to be borrowed from each bank, such that the family's objectives are realized.