Ace Electronics manufactures three different components for television sets. Component A requires 2 hours of fabrication and 1 hour of assembly

Component B requires 3 hours of fabrication and 1 hour of assembly

Component C requires 2 hours of fabrication and 2 hours of assembly.

The company has a maximum of 1,000 labor-hours of fabrication time and 800 labor - hours of assembly time available each week. The combined total number of components produced each week cannot exceed 420. The profit on each component A,B, and C is $7, $8, and $10 respectively. How many components of each type should the company manufacture each week in order to maximum its profit (assume that all components manufactured can be sold?) What is the maximum profit?