A plastic parts supplier produces two types of plastic parts used for electronics. Type 1 requires 1 hour of labor and 2 hours of machine time. Type 2 requires 2 hours of machine time and 3 hours of labor. There are 600 hours available per week of labor and 800 machine hours available. The demand for custom molds and plastic parts are identical. Type 1 has a profit margin of $30 a unit and Type 2 has a profit margin of $50 a unit. The plastic parts supplier must choose the quantity of Type 1 part and of Type 2 part to produce in order to maximize profit.

1. Formulate this as a linear programming problem.
2. Find the solution that gives the maximum profit.
3. What is the maximum profit?