A small bank offers three type of loans: housing loans at $8.50$% interest, education loans at $13.75$% interest rates, and loans to senior citizens at $12.25$% interest. Further, it needs to adhere to certain policy restrictions. The restrictions require the bank to ensure that Condition 1: housing loans make up between $25$% and $60$% of the total loan amount disbursed;and Condition 2: the amount of loans disbursed to senior citizens should be least one third of the total amount disbursed as loans. In a particular year, its lending capacity is $25,000,000\$$. The bank would like to disburse loans so as to maximize its earnings from the interest paid. Solve the problem graphically by taking two at a time.
From the problem, I derive the following LP model:
Decision variables:
$X_1:$ Amount disbursed as housing loan.
$X_2:$ Amount disbursed as education loan.
$X_3:$ Amount disbursed as loans to senior citizens.
Maximize $$0.085X_1 + 0.1375X_2 + 0.1225X_3$$
Subject to constraints:
$$X_1 \ge 625 \times 10^4$$ $$X_1 \le 150 \times 10^5$$ $$X_3 \ge \frac{25}{3} \times 10^6$$ where $X_1,X_2,X_3 \ge 0$
My question is: Is this formulation correct? and how to solve this three variable equations using graphical method. Precisely I don't understand "Solve the problem graphically by taking two at a time"
