Black Blend
Black Blend is a Brazilian company that produces, roasts, and distributes coffee grains to wholesalers.
The company owns three suppliers, Mineiro, Goiano, and Paulista. The procurement cost (production plus transportation) of raw grains from each supplier and the respective weekly availability is given in the table below.
| Supplier ID | Supplier | Procurement Cost ($/Kg) | Availability (Kg/Week) |
|---|---|---|---|
| 1 | Mineiro | 6.00 | 1000 |
| 2 | Goiano | 7.00 | 3000 |
| 3 | Paulista | 5.00 | 2000 |
Black Blend roasts and packs the grains in two facilities, Roast Bold and Hot Black. The processing cost and production capacity (maximum amount of raw grains that can be roasted per week) of each facility are given in the tables below.
| Factory ID | Factory | Processing Cost ($/Kg) | Capacity (Kg/Week) |
|---|---|---|---|
| 1 | Roast Bold | 10.00 | 2500 |
| 2 | Hot Black | 12.00 | 3000 |
Knowing that Black Blend sells roasted coffee for
\($25/Kg\), and that one kilogram of raw coffee
grains produces \(0.8Kg\) of roasted coffee,
how should they plan production to maximize their profit?