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 1,000 labor-hours of fabrication time and 750 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 x1, x2, and x3 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=7x1 + 8x2 + 10x3

subject to:

2x1+3x2+2x3<=1000

x1+ x2 + 2x3 <=750

x 1, x 2, x 3>=0

The company should manufacture _____ component As,_____component Bs, and

_____ component Cs to maximize their profit at $_____.