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A group of investors has $500,000 to invest and wants to ...

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A group of investors has $500,000 to invest and wants to maximize the money they will receive at the end of one year. They can invest in condos, apartments and houses. Furthermore, they wish to invest the entire amount. The profit after one year, the cost and the number of units available are shown below:

Investment Profit per unit Cost per unit # XXXXX
($1,000) ($1,000)
Condos 6 50 & nbsp; 10
Apartments 12 90 &n bsp; 5
Houses 9 100 7

a)Formulate the model for this problem.
b)What is the optimal solution?

The optimum profit is achieved by buying all 5 Apartments plus 1 Condo. The reason is as follows:

The profit margin on the apartments is the highest. i.e. 13.3%, (see the table below) so you invest as much as you can in Apartments. Since there are only 5 of them you will be spending 5 x $90,000 = $450,000, leaving $50,000.

Your next best profit category is the Condos (at 12%). So you invest the remaining $50,000 in Condos. That would buy you 1 Condo. The overall profit in this case is $66,000 which is 13.2% return on investment.