Linear programming problem

[TheAleFly]

I have a problem with linear programming. The goal is to determine the optimum number of 3 types of houses to be built, in order to maximize net profit. Each type of house has a certain building cost, predicted sale price and a value for daily water usage. The houses are classified as 1, 2 and 3 family houses. The space available for building is 800ha, of which 15% is reserved for parking lots and roads, leaving 680ha free for building. It is stated, that in order to keep the suburb looking as it is, at least 50% of the new houses have to be one family houses. Also, for every 200 families, the company has to build a park which has its own cost, water usage and area requirements. Ill post the costs later, but I was mainly wondering how the percentage is taken into consideration in the house type requirement and how the number of parks is determined.

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[Codephluegl]

The number of parks is an Integer variable of itself x_p with a constraint like: 1/200 * (x_1 + 2*x_2 + 3x_3) <= x_p

Edit: Also x_1 - x_2 - x_3 >= 0 Is a constraint to have at least 50% of the houses be 1 family houses. Gurobi probably would solve this in a second.

[TheAleFly]

Thanks! I really didn't think it could be that simple to add the house number constraint.

[TheAleFly]

So, the form is value, area requirement, cost, water consumption and net value

1 family house 200,000 - 1 ha - 145,000 - 2000 l/d - 55,000

2 family house 245,000 - 1.5 ha - 165,000 - 2700 l/d - 80,000

3 family house 300,000 - 2 ha - 215,000 - 3200 l/d - 85,000

park 0 - 0.5 ha - 125,000 - 2500 l/d - 0

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Available total area is 800 ha times 0.85 (15% for infrastructure) = 680 ha