5.7

import numpy as np  
  
demands = [40, 60, 80]  
max_production = 100  
total_demand = sum(demands)  
  
dp = np.full((4, total_demand + 1), float('inf'))  
dp[0][0] = 0  
  
prev_production = np.full((4, total_demand + 1), -1) 
  
for i in range(1, 4):  
    prev_demand = sum(demands[:i-1])  
    for j in range(total_demand + 1):  
        if j < prev_demand + demands[i-1]:  
            
            continue  
        for x in range(max(0, j - prev_demand - demands[i-1] + 1), min(max_production + 1, j - prev_demand + 1)):  
            production_cost = 50 * x + 0.2 * x**2  
            storage_cost = 4 * (j - prev_demand - x)  
            total_cost = dp[i-1][j-x] + production_cost + storage_cost  
            if total_cost < dp[i][j]:  
                dp[i][j] = total_cost  
                prev_production[i][j] = x  
   
min_cost = float('inf')  
final_state = -1  
for j in range(total_demand, total_demand + 1):  
    if dp[3][j] < min_cost:  
        min_cost = dp[3][j]  
        final_state = j  
  
production_plan = [0] * 3  
current_state = final_state  
for i in range(3, 0, -1):  
    production_plan[i-1] = prev_production[i][current_state]  
    current_state -= prev_production[i][current_state]  

print(f"最小总费用为: {min_cost} 元")  
print("生产计划为:")  
for i, plan in enumerate(production_plan, 1):  
    print(f"第{i}季度生产: {plan} 台")

print("学号：3004")