how to sparse matrix

In the example given under Intlinprog (factory, warehouse and sales outlet-matlab documenttation), one of the command to specify the sparse matrix is given as :Aineq = spalloc(P*F + W,matwid,P*F*W + S*W); i would please try to understand how the parameters for rows, and nonzero values have been arrived i.e P*F + W and P*F*W + S*W

Answer 1

[Massimo Zanetti]

According to the lines before alloc() call, https://it.mathworks.com/help/optim/ug/factory-warehouse-sales-allocation-model.html

there are

F = floor(f*N2); % number of factories
W = floor(w*N2); % number of warehouses
S = floor(s*N2); % number of sales outlets

and

P = 20; % 20 products

Therefore, to set up the linear system that defines inquality constraints they first allocate sparse matrix place

Aineq = spalloc(P*F + W,matwid,P*F*W + S*W)

and later they fill in the matrix.

[Sachin Kamble]

Massimor Thanks for your immediate reply.My question was pertaining to why? (P*F +W) for the rows and (P*F*W + S*W)for maximum non zeros. I understand that these are the variables defined in the problem. i am a little weak in permutations and combinations. i will be glad if you can please help me out. Can you please go through the codes and help me. please