Linopt1.py

gistfile1.txt

# Linear optimization example for the following
# optimization problem
#
# maximize:     z = x + 2y
# subject to:   2x + y <= 20
#               -4x + 5y <= 10
#               -x + 2y >= -2
#               -x + 5y = 15
#               x, y >= 0
#
# Modify problem to:
# minimize:     -z = -x - 2y
# subject to:   2x + y <= 20    (1)
#               -4x + 5y <= 10  (2)
#               x - 2y <= 2     (3)
#               -x + 5y = 15    (4)
#               x, y >= 0       (5)



from scipy.optimize import linprog

obj = [-1, -2]
#      ─┬  ─┬
#       │   └┤ Coefficient for y
#       └────┤ Coefficient for x


lhs_ineq = [[2, 1],         # constraint (1), left
            [-4, 5],        # constraint (2), left
            [1, -2]]        # constraint (2), left

rhs_ineq = [20,             # constraint (1), right
            10,             # constraint (2), right
            2]              # constraint (3), right

lhs_eq = [[-1, 5]]          # constraint (4), left
rhs_eq = [15]               # constraint (4), right

bnd = [(0, float("inf")),  # Bounds of x
       (0, float("inf"))]  # Bounds of y

opt = linprog(c=obj, A_ub=lhs_ineq, b_ub=rhs_ineq,
                  A_eq=lhs_eq, b_eq=rhs_eq, bounds=bnd,
                  method="simplex")

print(opt)