Hi,

let's go on with the example from https://www.linkedin.com/pulse/what-optimization-how-can-help-you-do-more-less-zoo-buses-fleischer/

Now let's see how easy it is to relax integrity constraints and turn a MIP into LP, solve and get dual value (shadow price)

def make_bus_model():
    mdl = Model(name='buses')
    nbbus40 = mdl.integer_var(name='nbBus40')
    nbbus30 = mdl.integer_var(name='nbBus30')

    mdl.add_constraint(nbbus40 * 40 + nbbus30 * 30 >= 300, 'kids')
    mdl.minimize(nbbus40 * 500 + nbbus30 * 400)
    return mdl

if __name__ == '__main__':
    bm1 = make_bus_model()
    bm1.print_information()
    s1 = bm1.solve(log_output=True)
    s1.display()

    bmr = make_relaxed_model(bm1)
    bmr.print_information()
    rs = bmr.solve(log_output=True)
    rs.display()

    duals = bmr.get_constraint_by_name("kids").dual_value

    print("dual of the 300 kids constraint = ",duals)

gives

solution for: buses
objective: 3800
nbBus40 = 6
nbBus30 = 2
Model: buses
 - number of variables: 2
   - binary=0, integer=0, continuous=2
 - number of constraints: 1
   - linear=1
 - parameters: defaults
CPXPARAM_Read_DataCheck                          1
Tried aggregator 1 time.
LP Presolve eliminated 1 rows and 2 columns.
All rows and columns eliminated.
Presolve time = 0.03 sec. (0.00 ticks)
solution for: buses
objective: 3750.000
nbBus40 = 7.500
dual of the 300 kids constraint =  12.5

And we can confirm that if we use only 40 seats buses the marginal cost of a seat within a 40 seats bus is costbus40/40=12.5

regards

PS: Many other very simple docplex examples at https://www.linkedin.com/pulse/making-optimization-simple-python-alex-fleischer/