Optimization giving unexpected results

Hi, I'm trying to optimize a function which I know the results but matlab is giving me weird results. Here's what I'm trying to do:

max: f(x)= 1815x1+379x2

subject to: -1475x1-112013x2 >= -700000

x1,,x2<=80

x1,x2>=0

How would you do it?

[Gimpy]

maybe I would like to do it with simplex method(My benchmark in Excel) or wahatever method is the best... thank you!

[Yu Jiang]

Can you share your code? Which built-in function are you using?

Bear in mind that both functions fminsearch and fmincon search for the minimum not the maximum.

-Yu

[Gimpy]

f = [1815;379]

A = [-1475 -11203]

b = [-700000]

ub= (ones(1,2)*80)'

lb = zeros(2,1)

x = linprog(f,A,b,[],[],lb,ub)

Answer 1

[Yu Jiang]

Hi Gimpy

Since linprog finds the minimum for the function f(x) but the problem you are trying to solve is a maximization problem, I suggest you change f = [1815;379] to f = -[1815;379]. That is to say, you solve the following problem instead

min: f(x)= - 1815x1 -379x2

subject to: -1475x1-112013x2 >= -700000

x1,,x2<=80

x1,x2>=0

There will only be a sign difference on the objective function. The optimal solutions x will be the same.

-Yu

[Gimpy]

tried that option, still not working

[Yu Jiang]

What is the expected answer?

[Gimpy]

x1=40 and x2 =80

[Gimpy]

Excel results.

[Yu Jiang]

Hi Gimpy

The answer seems not correct, since -1475*40 -11203*80 = -955240 <=700000, meaning the first inequality constraint is not satisfied.

Also, linprog treats inequality constraints as "<=" by default, not ">=". So your A and b matrices should be A = [1475 11203] and b = 700000

-Yu

[Gimpy]

Yes after a double check I realized it's my model that was mispecification not the matlab function that I don't understand. My understanding was correct. thank you