A small company manufactures three different electronic components for computers. Component A requires 2 hours of fabrication and 1 hour of​ assembly; component B requires 3 hours of fabrication and 1 hour of​ assembly; and component C requires 2 hours of fabrication and 2 hours of assembly. The company has up to ​labor-hours of fabrication time and ​labor-hours of assembly time available per week. 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 maximize its profit​ (assuming that all components manufactured can be​ sold)? What is the maximum​ profit?