$3-$ A factory has to install a smoke reduction system or pay a fine of $$10,000$ per month. The design of the system is outsourced to an A&E firm for $$60,000$ and takes six months to complete. The assembly, installation, and test are to be done on site. The cost of material is $$100,000,$ the cost of labor is $$60,000,$ and it takes eight months to bring the system to the operational level and avoid the penalty payment. The system needs an equivalent of one person at $$25,000$ per year to operate. The life of the system is five years, and the cost of