The steam that heats a factory is piped from a remote boiler. Insulation on the pipes will reduce the heat loss and thus reduce the heating cost. The heating cost for pipes with no insulation is 127,000 $/year. The reduction in heating costs for insulation x cm thick is heating cost saved with x cm of insulation = 12,000 x $/year The capital cost of the insulation is capital cost = fixed installation cost + material cost of insulation capital cost = 45,000 + $2, 1 00x^2 $ Because the pipes are exposed to the weather, the insulation must be replaced every three years. What thickness of insulation (if any) will maximize the ROI