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 1,100 labor-hours of fabrication time and 900 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? Let x_1, X_2, and x_3 be the numbers of components A, B, and C, respectively, that get manufactured. Construct a mathematical model in the form of a linear programming problem. Maximize p = 7X_1 + 8x_2 + 10x_3 subject to 2X_1 + 3X_2 + 2X_3 lessthanorequalto 1100 Fabrication time restriction X_1+X_2 + 2x_3 lessthanorequalto 900 Assembly time restriction X_1, x_2, x_3 greaterthanorequalto 0 The company should manufacture component As, component Bs, and component Cs to maximize their profit at $.