the question is on linear programming problems

3 次查看（过去 30 天）

TYSON 2024-2-17

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2083123-the-question-is-on-linear-programming-problems

评论： TED MOSBY 2024-9-2

A farm manufacturers three products P1, P2 and P3 using two machines M1 and M2. The product yield a contribution of sh.3 sh.2 and sh.4 respectively. Machine M1 and M2 have 2000 and 2500 machine hours respectively. There is an agreement with trading association to manufacture at least 100 units of P1, 200 units of P2 and 50 units of P3 but not more than 150 units of P1. The table below shows the processing time in hours for each machine on each product.

products

machines P1 P2 P3

M1 4 3 5

M2 2 2 4

required:

i. The production plan that maximizes contribution

3 个评论
显示 1更早的评论隐藏 1更早的评论

Torsten 2024-2-17

Where do you encounter difficulties ? Deriving objective function and constraints ? Or solving the problem ?

If it's the first: We won't help.

If it's the latter: Use MATLAB's "linprog".

Steven Lord 2024-2-17

This sounds like a homework assignment. If it is, show us the code you've written to try to solve the problem and ask a specific question about where you're having difficulty and we may be able to provide some guidance.

If you aren't sure where to start because you're not familiar with how to write MATLAB code, I suggest you start with the free MATLAB Onramp tutorial to quickly learn the essentials of MATLAB.

If you aren't sure where to start because you're not familiar with the mathematics you'll need to solve the problem, I recommend asking your professor and/or teaching assistant for help.

请先登录，再进行评论。

请先登录，再回答此问题。

回答（1 个）

TED MOSBY 2024-8-25

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2083123-the-question-is-on-linear-programming-problems#answer_1504729

编辑：TED MOSBY 2024-8-25

在 MATLAB Online 中打开

Hi @TYSON,

To get the optimal production plan, you can implement this using MATLAB’s function “linprog”.

Assuming you have the objective functions, inequality constraints and the lower and upper bounds. Here is an example code for the same:

% Coefficients for the objective function (negative for maximization) 
f = [-3, -2, -4]; 
% Coefficients for the inequality constraints 
A = [4, 3, 5; 2, 2, 4]; 
b = [2000; 2500]; 
% Coefficients for the lower and upper bounds 
lb = [100, 200, 50]; 
ub = [150, Inf, Inf]; 
% Solve the linear programming problem 
options = optimoptions('linprog', 'Display', 'off'); 
[x, fval] = linprog(f, A, b, [], [], lb, ub, options); 
% Display the results 
disp('Optimal Production Plan:'); 
fprintf('P1: %.2f units\n', x(1)); 
fprintf('P2: %.2f units\n', x(2)); 
fprintf('P3: %.2f units\n', x(3)); 
fprintf('Maximum Contribution: Sh. %.2f\n', -fval); 

Here is the documentation for the "linprog" and the "optimoptions" functions:

www.mathworks.com/help/optim/ug/linprog.html? searchHighlight=linprog&s_tid=srchtitle_support_results_1_linprog

www.mathworks.com/help/optim/ug/optim.problemdef.optimizationproblem.optimoptions.html?searchHighlight=optimoptions&s_tid=srchtitle_support_results_1_optimoptions

Hope this helps!

7 个评论
显示 5更早的评论隐藏 5更早的评论

Torsten 2024-9-1

编辑：Torsten 2024-9-1

在 MATLAB Online 中打开

@KALASH

max: 3*(x11+x12) + 2*(x21+x22) + 4*(x31+x32)
s.t.
4*x11 + 3*x21 + 5*x31 <= 2000
2*x12 + 2*x22 + 4*x32 <= 2500
x11 + x12 >= 100
x11 + x12 <= 150
x21 + x22 >= 200
x31 + x32 >= 50
x11 >= 0
x12 >= 0
x21 >= 0
x22 >= 0
x31 >= 0
x32 >= 0