Vollmer Manufacturing makes three components for sale to refrigeration companies. The components are processed on two machines: a shaper and a grinder. The times (in minutes) required on each machine are as follows.
| Machine | ||
| Component | Shaper | Grinder |
| 1 | 6 | 4 |
| 2 | 4 | 5 |
| 3 | 4 | 2 |
The shaper is available for 120 hours, and the grinder is available for 110 hours. No more than 200 units of component 3 can be sold, but up to 1000 units of each of the other components can be sold. In fact, the company already has orders for 600 units of component 1 that must be satisfied. The profit contributions for components 1, 2, and 3 are $8, $6, and $9, respectively.
a. Provide the mathematical formulation for this problem. Carefully define your decision variables, objective function, model constraints, and non-negativity statement.
