Implement and solve the "PQR Product Mix" problem discussed in class (LP below) using Python and Gurobi.
max 45x1 + 60x2 + 50x3
subject to: 20x1 + 10x2 + 10x3 ≤2400
12x1 + 28x2 + 16x3 ≤2400
15x1 + 6x2 + 16x3 ≤2400
10x1 + 15x2 + 0x3 ≤2400
x1 ≤100
x2 ≤40
x3 ≤60
x1 ≥0
x2 ≥0
x3 ≥0