As the chief engineer in charge of a proposed major civil engineering structure in your country's capital, you have a fiduciary responsibility to optimize the use of taxpayer dollars in maintaining the system. You have been tasked with developing a maintenance program for the new system from now (year 0) until the end of its service life in 75 years. For each year of this horizon period, you seek to determine whether or not to undertake some repair activity. There are three categories of repair that you could undertake: major maintenance, minor maintenance, or simple routine maintenance. Every year, you need to apply only one of these repair categories. Each repair category has an associated benefit and cost. You seek to maximize the ratio of total benefits to total costs over the life cycle. The overall maintenance budget over the life cycle is $C. Other constraints are that the total benefit must be at least a certain threshold, R units.
(a) What kind of knapsack problem is exemplified by this problem? Give reason for your answer.
(b) Using suitable decision variables, write a simple but complete mathematical formulation for this optimization problem.