CAPITAL RATIONNING CASE STUDY
This is taken from the book by Salkin and Kornbluth “Linear Programming and Financial Planning”.
A capitalist has some money to spare. The amount available changes from year to year and is given in the table below. This
money can be invested in six projects. The annual cost of each project, having taken into account expenditure and income, is
also given in the table.
Project 1 2 3 4 5 6 Available Borrow Lend
Year 1 12 54 6 6 30 6 35 B1L1
Year 2 3 10 6 2 35 10 35 B2L2
Year 3 5 4 6 5 10 4 20 B3L3
Final value 44 70 35 35 88 35
Share X1X2X3X4X5X6
The table also gives the final value of the project.
The capitalist can invest in the complete project or share it with other capitalists, but once the share of the project has been taken
into account, it cannot be changed during the first three years.
It is also possible to borrow money from the bank, or to place at interest any residual savings. The borrowing rate from the bank
is 9%, and deposits can achieve 4%.
In which projects must the capitalist invest and in which proportion in order to maximize her/his final wealth?
Resolution
1) Decision variables: