The fixed cost for a steam line per meter of pipe is $450 X + $50 per year. The cost for loss of heat from the pipe per meter is $4.8/X^1/2 per year. Here, X represents the thickness of insulation in meters, and X is a continuous design variable.
a. What is the optimum thickness of the insulation?
b. How do you know that your answer in Part (a) minimizes total cost per year?
c. What is the basic trade-off being made in this problem?