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 950 labor-hours of fabrication time and 700 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? Answer: The company should manufacture Component As, Component Bs, and component Cs To maximize their profit at $

Step 1 ：This is a linear programming problem. We need to maximize the profit function subject to the constraints of available labor hours for fabrication and assembly.

Step 2 ：The profit function is \(7A + 8B + 10C\), where A, B, and C are the number of components A, B, and C to be manufactured.

Step 3 ：The constraints are \(2A + 3B + 2C \leq 950\) (fabrication time) and \(A + B + 2C \leq 700\) (assembly time).

Step 4 ：We also have the constraints \(A \geq 0\), \(B \geq 0\), and \(C \geq 0\) since we can't manufacture a negative number of components.

Step 5 ：We can solve this problem using a linear programming solver.

Step 6 ：The optimal solution given by the linear programming solver is to manufacture 250 units of component A, 0 units of component B, and 225 units of component C.

Step 7 ：The maximum profit is $4000.

Step 8 ：Final Answer: The company should manufacture \(\boxed{250}\) component As, \(\boxed{0}\) component Bs, and \(\boxed{225}\) component Cs to maximize their profit at \(\boxed{\$4000}\).