A simultaneous linear equation usually will consist of two types of equation(I will be using a fundraiser event as an example), which are the parameters(budget, deadlines, location) and a value to be maximized(i.e. the money raised). Normally we would solve these types of equations in MATLAB using the command simlp. From what I understand, simlp requires three different vectors to use. A and b, which represents the parameters for the problem, and f, represents the function of the maximized value. Now my question is, why are the values in vector f always negative, while some values of vector A and b still can remain positive? Attached below is a sample question.
We let w, x, y, and z, denote the number of residences canvassed in the four cities Gotham, Metropolis, Oz, and River City, respectively.
Then the linear inequalities specified by the given data are as follows:
Nonnegative data: w ≥ 0, x ≥ 0, y ≥ 0, z ≥ 0;
Pamphlets: w + x + y + z ≤ 50,000; T
ravel cost: 0.5w + 0.5x + y + 2z ≤ 40,000;
Time available: 2w + 3x + y + 4z ≤ 18,000;
Preferences: w ≤ x, x + y ≤ z; 282
Contributions: w + 0.25x + 0.5y + 3z ≥ 10,000.
The quantity to be maximized is: Voter support: 0.6w + 0.6x + 0.5y + 0.3z.
The vector form is as follows:
f = [-0.6 -0.6 -0.5 -0.3];A = [1 1 1 1; 0.5 0.5 1 2; 2 3 1 4; 1 -1 0 0; 0 1 1 -1; -1... -0.25 -0.5 -3; -1 0 0 0; 0 -1 0 0; 0 0 -1 0; 0 0 0 -1];b = [50000; 40000; 18000; 0; 0; -10000; 0; 0; 0; 0];
Best Answer