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
50,000x1 + 12,000x2 + 8,000x3 < $250,000
x1 < 4 condominiums
x2 < 15 acres
x3 < 20 bonds
x2 > 0
x1, x3 > 0 and integer
x1 = condominiums purchased
x2 = acres of land purchased
x3 = bonds purchased