用matlab解决这个问题并给出代码
时间: 2023-08-28 17:03:36 浏览: 30
以下是用MATLAB编写的线性规划问题代码。
```matlab
% Define transportation problem data
% Demand matrix for each city and service level
d = [60 40 30 70 90; 30 40 50 20 30; 80 90 60 40 50; 50 60 30 20 10];
% Transportation capacity matrix for each city pair and service level
c = [50 80 70 60 90; 30 60 50 70 40; 60 80 90 50 70; 80 50 60 40 30];
% Transportation cost per unit weight for each service level
p = [8 6 4 2];
% Define linear programming problem
f = [p(1)*ones(1,15) p(2)*ones(1,15) p(3)*ones(1,15) p(4)*ones(1,15)];
Aeq = zeros(20,60);
beq = zeros(20,1);
lb = zeros(60,1);
% Define demand constraints
for i = 1:4
for k = 1:4
Aeq(i+(k-1)*4,(i-1)*15+(k-1)*5+1:i*15+(k-1)*5) = ones(1,15);
beq(i+(k-1)*4) = d(i,k);
end
end
% Define capacity constraints
for k = 1:4
for i = 1:5
for j = 1:5
Aij = zeros(1,60);
Aij((i-1)*15+(j-1)*3+(k-1)+1) = 1;
Aeq = [Aeq; Aij];
beq = [beq; c(i,j,k)];
end
end
end
% Solve linear programming problem
[x, fval] = linprog(f,[],[],Aeq,beq,lb);
% Reshape solution vector to matrix form
x = reshape(x,15,4);
% Print solution matrix
disp("Transportation plan:");
disp(x);
```
代码中使用了MATLAB中的`linprog`函数来解决线性规划问题。在代码中,我们首先定义了运输问题的数据,包括需求矩阵、运输容量矩阵和运输成本。然后,我们定义了线性规划问题,包括目标函数、约束条件和决策变量。在约束条件中,我们为需求约束和容量约束分别定义了约束条件。最后,我们使用`linprog`函数来解决线性规划问题,并将解决方案转换为矩阵形式进行输出。