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("2023310143005")
