f(x，y)=(16800 - 71.8*x +55.9*y - 6000)*x + 10.4*y + 4400使用matlab求在限制条件-71.8x+5.375y＜0下最大值

可以使用Matlab中的线性规划函数 `linprog` 来求解该问题。具体步骤如下：

1. 将目标函数转化为标准形式：将目标函数转化为最小化形式，并将所有不等式约束转化为小于等于形式。

minimize: -16800x + 71.8x^2 - 55.9xy + 6000x
          - 10.4y - 4400
subject to: -71.8x + 5.375y <= 0

2. 将目标函数和约束条件转化为Matlab函数中的矩阵形式。

f = [-16800, 71.8, -55.9, 6000, -10.4, -4400];
A = [-71.8, 5.375];
b = [0];

3. 调用 `linprog` 函数求解最优解。

[x, fval] = linprog(f, [], [], A, b);

其中，`x` 为最优解向量，`fval` 为最优解的目标函数值。

根据上述步骤，可以得到以下Matlab代码：

f = [-16800, 71.8, -55.9, 6000, -10.4, -4400];
A = [-71.8, 5.375];
b = [0];

[x, fval] = linprog(f, [], [], A, b);

disp(['最大值为：', num2str(-fval)]);

运行上述代码即可得到在限制条件 `-71.8x + 5.375y < 0` 下的最大值。

相关问题

function [x_opt, y_opt, f_opt] = maximize_profit() % 定义目标函数 f = @(x, y) -(16800 - 71.8*x +55.9*y - 6000)*x + 10.4*y + 4400; % 定义约束条件 lb = [-inf, -inf]; ub = [inf, inf]; Aeq = []; beq = []; Aineq = []; bineq = []; % 使用 fmincon 函数求解最优解 [x_opt, f_opt] = fmincon(@(x) f(x(1), x(2)), [0, 0], Aineq, bineq, Aeq, beq, lb, ub); y_opt = (16800 - 71.8*x_opt - 6000) / (-55.9); % 输出结果 fprintf('最优解为 x = %.4f，y = %.4f，最大值为 %.4f\n', x_opt, y_opt, -f_opt); end给此代码加入限定条件(-71.8x+5.375y＜0)

可以将新的限定条件加入到 Aineq 和 bineq 中，如下所示：

function [x_opt, y_opt, f_opt] = maximize_profit()
% 定义目标函数
f = @(x, y) -(16800 - 71.8*x +55.9*y - 6000)*x + 10.4*y + 4400;

% 定义约束条件
lb = [-inf, -inf];
ub = [inf, inf];
Aeq = [];
beq = [];
Aineq = [-71.8, 5.375];
bineq = [0];

% 使用 fmincon 函数求解最优解
[x_opt, f_opt] = fmincon(@(x) f(x(1), x(2)), [0, 0], Aineq, bineq, Aeq, beq, lb, ub);

y_opt = (16800 - 71.8*x_opt - 6000) / (-55.9);

% 输出结果
fprintf('最优解为 x = %.4f，y = %.4f，最大值为 %.4f\n', x_opt, y_opt, -f_opt);
end

ValueError: x and y must have same first dimension, but have shapes (89,) and (87, 1)

This error occurs when you are trying to plot a graph with two arrays of different sizes. In this case, the x array has 89 elements and the y array has 87 elements.

To fix this error, you need to make sure that the x and y arrays have the same number of elements. One possible solution is to modify the y array by adding or removing some elements to match the size of the x array.

Another solution is to reshape the y array so that it has the same number of rows as the x array. You can do this by using the numpy.reshape() function as follows:

import numpy as np

x = np.array([1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89])
y = np.array([3.2, 4.5, 5.7, 6.8, 7.9, 9.0, 10.1, 11.2, 12.3, 13.4, 14.5, 15.6, 16.7, 17.8, 18.9, 19.0, 20.1, 21.2, 22.3, 23.4, 24.5, 25.6, 26.7, 27.8, 28.9, 30.0, 31.1, 32.2, 33.3, 34.4, 35.5, 36.6, 37.7, 38.8, 39.9, 41.0, 42.1, 43.2, 44.3, 45.4, 46.5, 47.6, 48.7, 49.8, 50.9, 52.0, 53.1, 54.2, 55.3, 56.4, 57.5, 58.6, 59.7, 60.8, 61.9, 63.0, 64.1, 65.2, 66.3, 67.4, 68.5, 69.6, 70.7, 71.8, 72.9, 74.0, 75.1, 76.2, 77.3, 78.4, 79.5, 80.6, 81.7, 82.8, 83.9, 85.0, 86.1, 87.2, 88.3, 89.4, 90.5, 91.6, 92.7, 93.8, 94.9, 96.0])

# Reshape y array to have the same number of rows as x array
y = y.reshape(-1, 1)

# Plot the graph
import matplotlib.pyplot as plt
plt.plot(x, y)
plt.show()

This code will reshape the y array to have 89 rows and 1 column, so that it has the same number of elements as the x array. The graph will then be plotted without any errors.