ExtremeBikes produces professional helmets. The helmet's outer shell is made of composite materials that contain Carbon, Kevlar, and Polycarbonate. The company has a contract for helmets, with shells that must weigh 1.7 lb each, from which at least 20% must be carbon, at least 15% of the shell must be Kevlar and no more than 50% of the shell must be Polycarbonate. The sum of Carbon, Kevlar and Polycarbonate must equal 1.7 lb. Costs are: Carbon $7.50/lb, Kevlar $14/lb, Polycarbonate $2.50/lb. The objective is to determine the amounts of Carbon, Kevlar, and Polycarbonate to be used in each helmet shell that will minimize total material cost.

1.) What is the objective function?

2.) What are the constraints for carbon, kevlar, polycarbonate, and the shell?

3.) What is the non-negativity?

4.) Set up the problem on a separate sheet and solve the problem using solver on excel