A home buyer in France can combine several mortgage loans to finance the purchase of a house. Given borrowing needs B and a horizon of T months for paying back the loans, the home buyer would like to minimize his total cost (or equivalently, the monthly payment p made during each of the next T months). Regulations impose limits on the amount that can be borrowed from certain sources. There are n different loan opportunities available. Loan i has a fixed interest rate ri, a length Ti ≤ T and a maximum amount borrowed bi. The monthly payment on loan i is not required to be the same every month, but a minimum payment mi is required each month. However the total monthly payment p over all loans is constant. Formulate a linear program that finds a combination of loans that minimizes the home buyer’s cost of borrowing.

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