import numpy as np
from scipy.optimize import linprog


cost = np.array([4.0, 7.0])

# Demand: regular + premium = 10
A_eq = np.array([(1.0, 1.0)])
b_eq = np.array([10.0])

# Quality: regular + 2 * premium >= 14
A_ub = np.array([(-1.0, -2.0)])
b_ub = np.array([-14.0])

bounds = [(0.0, None), (0.0, None)]

result = linprog(
    c=cost,
    A_ub=A_ub,
    b_ub=b_ub,
    A_eq=A_eq,
    b_eq=b_eq,
    bounds=bounds,
    method="highs",
)

regular, premium = result.x
quality_points = regular + 2.0 * premium

print(f"success: {result.success}")
print(f"message: {result.message}")
print(f"minimum_cost: {result.fun:.2f}")
print(f"regular_units: {regular:.1f}")
print(f"premium_units: {premium:.1f}")
print(f"quality_points: {quality_points:.1f}")
print(f"demand_residual: {result.eqlin.residual[0]:.2e}")
print(f"quality_slack: {result.ineqlin.residual[0]:.2e}")