Shipping from Minimize Number of Warehouses while generating shipping plans

Question

I'm working to figure out an algorithm to solve the problem below:

• There are w warehouses that store p different products with different quantities
• A customer places an order on n out of the p products

For example:

                Product 1 |  Product 2 | Product 3
Warehouse A   |     1     |      2     |    1    |
Warehouse B   |     2     |      2     |    1    |
Warehouse C   |     2     |      1     |    5    |

Customer ordered: 2 X Product 1, 2 X Product 2, and 3 Product 3.

I searched and found this similar question:(Minimizing the number of warehouses for an order)

I followed the ILP solution:

import numpy as np
from ortools.linear_solver import pywraplp


# Some test data, replace with your own.
p = 50
w = 1000
n = np.random.randint(0, 10, p)
C = np.random.randint(0, 5, (w, p))

solver = pywraplp.Solver("model", pywraplp.Solver.CBC_MIXED_INTEGER_PROGRAMMING)
x = [solver.BoolVar(f"x[{i}]") for i in range(w)]
    
for j in range(p):
    solver.Add(C[:, j] @ x >= n[j])
    
solver.Minimize(sum(x))

assert solver.Solve() is not None
    
print("Solution:")
print(f"assigned = {[i + 1 for i in range(len(x)) if x[i].solution_value()]}")
print(f"     obj = {solver.Objective().Value()}")
print(f"    time = {solver.WallTime() / 1000}s")

It is giving me the result of which warehouses are chosen to ship out the items. But I need solution that will tell each warehouse how many of what items to be shipped. I think it will involve solution of matrices.

Anyone can point me to the right direction of solving this? Much appreciated.