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