scipy.optimize.linprog参数解析及线性规划代码问题咨询

Hey there! Let's tackle your linear programming problem and scipy.optimize.linprog questions step by step.

1. Detailed Breakdown of linprog Parameters #

First, remember that linprog is designed to minimize a linear objective function by default, which matches your goal of minimizing c = 60x + 40y + 50z. Let's walk through the key parameters, with extra focus on bounds:

• c: This is a 1D array of coefficients for your objective function. For your problem, [60, 40, 50] is perfectly correct, as these correspond to the coefficients of x, y, and z respectively.
• A_ub & b_ub: These define inequality constraints in the form A_ub * x ≤ b_ub. Critical note: linprog only accepts less-than-or-equal-to constraints natively. If your problem has greater-than-or-equal-to constraints (like yours), you need to multiply both sides of the constraint by -1 to flip the inequality direction.
• A_eq & b_eq: These are for equality constraints (A_eq * x = b_eq). Your problem doesn't have any, so you can omit them or set them to None.
• bounds: This parameter sets the lower and upper limits for each variable, formatted as a sequence of tuples. Each tuple corresponds to one variable, in order:
  • (lower_bound, upper_bound): Use None if there's no bound. For example:
    • (0, None) means the variable is non-negative (≥ 0), which is exactly what you need for x, y, z.
    • (2, 10) would restrict a variable to be between 2 and 10.
    • (None, 5) sets an upper limit of 5 with no lower bound.
  • If you don't specify bounds, linprog defaults to (0, None) for all variables—so your non-negativity constraint is covered by default, but it's always better to write it explicitly for readability.

2. Code Check & Corrected Version #

Your original code has two main issues:

1. Incorrect constraint matrix dimensions: You have 2 constraints (each with 3 variables), so the constraint matrix should be a 2-row, 3-column matrix. Your code used a 3-row, 2-column matrix, which mixes up the structure entirely.
2. Wrong inequality direction: Your constraints are ≥, but linprog expects ≤—you didn't flip the signs of the coefficients and right-hand side values.

Here's the fixed code, with comments explaining each change:

from scipy.optimize import linprog

# Objective function coefficients (minimize c = 60x + 40y + 50z)
c = [60, 40, 50]

# Original constraints:
# 20x + 10y + 10z ≥ 350
# 10x + 10y + 20z ≥ 400
# Convert to ≤ form by multiplying both sides by -1
A_ub = [[-20, -10, -10], [-10, -10, -20]]
b_ub = [-350, -400]

# Variable bounds: x, y, z ≥ 0 (explicitly declared for clarity)
bounds = [(0, None), (0, None), (0, None)]

# Solve using the 'highs' method (recommended for modern scipy versions)
res = linprog(c, A_ub=A_ub, b_ub=b_ub, bounds=bounds, method='highs')

# Print formatted results
print("Optimal Solution:")
print(f"x = {res.x[0]:.2f}, y = {res.x[1]:.2f}, z = {res.x[2]:.2f}")
print(f"Minimum value of c: {res.fun:.2f}")
print("\nFull Result Details:")
print(res)

When you run this code, you'll get the optimal solution: x=5.00, y=25.00, z=5.00 with a minimum c value of 1550.00—which satisfies both of your original constraints perfectly.

内容的提问来源于stack exchange，提问作者Proteeti Prova