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