A Mixed Integer Model Example

 

 

Nancy Smith has $250,000 to invest in three alternative investments – condominiums, land, and municipal bonds.  She wants to invest in the alternatives that will result in the greatest return on investment after one year.

 

Each condominium costs $50,000 and will return a profit of $9,000 if sold at the end of one year; each acre of land costs $12,000 and will return a profit of $1,500 at the end of one year; and each municipal bond costs $8,000 and will result in a return of $1,000 if sold at the end of one year.  In addition, there are only 4 condomininums, 15 acres of land, and 20 municipal bonds available for purchase.

 

The linear programming model for this problem is formulated as follows.

 

            maximize Z = $9,000x1 + 1,500x2 + 1,000x3

 

            subject to

 

                        50,000x1 + 12,000x2 + 8,000x3 < $250,000

                                                                           x1 < 4 condominiums

                                                                           x2 < 15 acres

                                                                           x3 < 20 bonds

                                                                           x2 > 0

                                                                    x1,  x3 > 0 and integer

 

            where

 

            x1 = condominiums purchased

            x2 = acres of land purchased

            x3 = bonds purchased