Problem: You have up to $250,000 to invest in three alternative investments--condominiums, land, and municipal bonds. 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.

Each municipal bond costs $8,000 and will result in a return of $1,000 if sold at the end of one year.

There are only 4 condominiums, 15 acres of land, and 20 municipal bonds available for purchase. Note that you can only purchase whole condominiums and whole bonds (you cannot purchase a fraction of a condo or a bond). In addition, you do not want to have more than 50% of your total investment in condominiums. If you wish to invest in the alternatives that will result in the greatest return on investment after one year, how should you invest your money?

You do not need to solve this problem, just set it up.

 

a. What are your decision variables (x)? State the units for each?

 

b. Write down your objective function (include min/max with the equation) and constraints below, include descriptions/explanations.