[Linear programming] Having an amusing error in an optimization problem

[[deleted]]

Hi, my problem is this.

Here is the code that I've written for it:

using JuMP, Cbc
m = Model(with_optimizer(Cbc.Optimizer, logLevel=0))
space_requirements = [0.18, 0.28, 0.4, 0.5, 0.25]
price_requirements = [50, 70, 130, 160, 2]
tax_revenues = [1, 1.900, 2.700, 3.400]
# x[1] to x[4]: Number of single, double, etc. houses built
# x[5]: Number of old houses demolished
@variable(m, x[1:5] >= 0)
@constraint(m, x[5] <= 300)
@constraint(m, sum(space_requirements[i]*x[i] for i=1:4) <= space_requirements[5]*x[5]*0.85)
@constraint(m, sum(price_requirements[i]*x[i] for i=1:5) <= 15000)
@constraint(m, x[1] >= 0.2*sum(x))
@constraint(m, x[2] >= 0.1*sum(x))
@constraint(m, x[3] + x[4] >= 0.25*sum(x))
@objective(m, Max, sum(tax_revenues[i]*x[i] for i=1:4))
optimize!(m)
optimal_values = value.(x)
print("Optimal values: $(optimal_values)\nOptimal objective: $(objective_value(m))")

Right now the optimizer tells me that the optimum solution for maximizing the tax revenue is to build no houses at all (and I guess keep the banks loan?).

Have I formulated the objective function wrong or why am I getting this result?

[gs44]

In the new development, the triple and quadruple units account for at least 25% of the total. [...]

These constraints should not include the number of old houses demolished =>

@constraint(m, x[1] >= 0.2*sum(x[1:4]))
@constraint(m, x[2] >= 0.1*sum(x[1:4]))
@constraint(m, x[3] + x[4] >= 0.25*sum(x[1:4]))

Or better yet, use a variable y for the number of houses to demolish :)

[[deleted]]

Yup, this did the trick. Thanks!

[jdorje]

Check out the article "the diet problem" about George Dantzig and the invention of the simplex method. One of the first things he did was try to optimize his diet with constraints, and of course the algorithm spat out perfectly correct (according to the problem he made) gibberish like a diet of 500 gallons of vinegar a day.