Solving goal programming problem with MATLAB

Please, can someone help me chech what is wrong with my code for the problem below:

Question:

Solve the following goal programming problem given below

objective 1 (yield goal)

208*x(1)^0.323168*x(2)^0.172084*x(3)^0.085998*x(4)^0.188794*x(5)^0.229956 >= 6611

objective 2 (budget goal)

2.8*x(1)+22*x(2)+4*x(3)+0.272*x(4)+x(5) <= 492

Objective 3 (Chemical goal)

22*x(2)+4*x(3) <= 212

Objective 4 (Seed goal)

x(4) <= 70

Weights = [0.5 0.17 0.13 0.25]

Solution:

fun = @(x)[208*x(1)^0.323168*x(2)^0.172084*x(3)^0.085998*x(4)^0.188794*x(5)^0.229956;2.8*x(1)+22*x(2)+4*x(3)+0.272*x(4)+x(5);22*x(2)+4*x(3)];

goal = [6611,492,212,70];

weight = [0.5,0.17,0.13, 0.25];

x0 = [3000,2000,100,35];

x = fgoalattain(fun,x0,goal,weight)

Error Message:

Index exceeds matrix dimensions.

Error in

@(x)[208*x(1)^0.323168*x(2)^0.172084*x(3)^0.085998*x(4)^0.188794*x(5)^0.229956;2.8*x(1)+22*x(2)+4*x(3)+0.272*x(4)+x(5);22*x(2)+4*x(3)]

Error in goalcon (line 64)

f = feval(funfcn{3},x,varargin{:});

Error in fgoalattain (line 406)

[ctmp,ceqtmp] = feval(cfun{3},xnew,extravarargin{:});

Caused by:

Failure in initial user-supplied objective function evaluation. Optimization cannot continue.

Answer 1

[Torsten]

x0 must be a vector of size 1x5, not 1x4.

Further, your function must return a vector of length 4, not 3.

Further, the first objective must be multiplied by (-1) in order to get <= instead of >=.

fun = @(x)[-208*x(1)^0.323168*x(2)^0.172084*x(3)^0.085998*x(4)^0.188794*x(5)^0.229956;2.8*x(1)+22*x(2)+4*x(3)+0.272*x(4)+x(5);22*x(2)+4*x(3);x(4)];
goal = [-6611,492,212,70];
weight = [0.5,0.17,0.13, 0.25];
x0 = [3000,2000,100,35,22];
x = fgoalattain(fun,x0,goal,weight)

Local minimum possible. Constraints satisfied.

fgoalattain stopped because the size of the current search direction is less than
twice the value of the step size tolerance and constraints are 
satisfied to within the value of the constraint tolerance.

x = 1×5

1.0e+03 * 3.0000 1.8302 0.0691 0.0350 0.0220

Answer 2

[John D'Errico]

READ THE ERROR MESSAGE! What did it say?

"Failure in initial user-supplied objective function evaluation. Optimization cannot continue."

Surely that was returned for a reason. Here was your code:

fun = @(x) [208*x(1)^0.323168*x(2)^0.172084*x(3)^0.085998*x(4)^0.188794*x(5)^0.229956;2.8*x(1)+22*x(2)+4*x(3)+0.272*x(4)+x(5);22*x(2)+4*x(3)];
x0 = [3000,2000,100,35];

Now, a thing I always strongly suggest when someone uses an optimizer, is to test to see if the objective function even works.

fun(x0)

Index exceeds the number of array elements. Index must not exceed 4.

Error in solution>@(x)[208*x(1)^0.323168*x(2)^0.172084*x(3)^0.085998*x(4)^0.188794*x(5)^0.229956;2.8*x(1)+22*x(2)+4*x(3)+0.272*x(4)+x(5);22*x(2)+4*x(3)] (line 1)
fun = @(x) [208*x(1)^0.323168*x(2)^0.172084*x(3)^0.085998*x(4)^0.188794*x(5)^0.229956;2.8*x(1)+22*x(2)+4*x(3)+0.272*x(4)+x(5);22*x(2)+4*x(3)];

Now, why might that fail? Your objective is a function of FIVE unkowns. Yet you gave it only 4 starting values.

[Ezra]

Thank you all for your observations, comments and solutions. I would take time to go over them and do all the necessary amendment.

Merci beaucoup