A nationalized bank has launched a new hassle-free scheme where government employees can apply for a fixed amount and duration housing loans or car loans. This scheme will be open for application for a week only, during upcoming festival season. A Housing loan would be for Rs. 10,00,000 and a car loan would be for Rs. 4,00,000; both repayable within 5 years. These are expected to give the bank a profit of Rs. 50,000 and Rs. 30,000 respectively. One branch has received many loan applications under both categories. The branch can consider only a limited number due to the following reasons. The branch-manager has estimated that for processing housing loan it takes 5 man hours and for car-loan 3 man-hours are required. The branch can allow 300 man-hours per week for this job. Moreover, the branch has a limit of Rs. 1,00,00,000 for total disbursement under this scheme. Find out the optimal number of loans to be processed by the branch which would maximize the profit. (iii) First formulate and solve the problem assuming fractional values for decision variables are allowed? Will your solution change if it is specified that the decision variables can take integer values only? What are integer programming problems and how they are solved?