Start by introducing variables for the amounts of dollars that the bank lends to the various categories, say v, w, x, y, z for Personal, Car, Home, Farm, Commercial respectively. The total amount lent is 12 million, so v+w+x+y+z = 12,000,000.

The objective function (to be maximised) is the net return, which you calculate like this. For Personal loans, out of the total amount v dollars that the bank lends, there will be an income of 0.14v in interest (in a one-year period *). There will be a loss of 0.1v in bad debts (presumably that's also in a one-year period, though the question doesn't say so *). So the net income to the bank will be 0.04v. For the other four forms of loan, you can work out the net income in the same way, then add all five income streams together to get the objective function.

There are some constraints on the different forms of loans. You need to translate these into inequalities among the variables v, w, x, y, z. Then use the simplex method to maximise the objective function subject to those constraints.

* Note. As so often seems to happen, this is a badly worded problem. The bank's income from the five forms of loan is given in terms of interestrates, in other words the income per year. It doesn't tell you anywhere in the question that you should maximise the income over aone-year period, but that is what you have to assume in order to be able to do the problem.