A local asset management agency oversees the repair and replacement of the highway infrastructure system. The annual budget allocations are $50,000,000 for asset repair and replacement. Assets can be upgraded to satisfy GASB 34 requirements either by minor repair, resurfacing, or replacement,. The minor repair related cost is $140,000 per linear-mile of roads, resurfacing cost is $450,000 per linear-mile, and replacement cost is $1,500,000 per linear-mile of roads. You are required to replace at least 15 linear-mile of roads and repair at least 30 linear-mile of roads. Roads replaced, resurfaced, or repaired must be in whole miles (sliver replacement or repair is not be allowed). Each linear-mile of new road is credited with 20 years of service life, each linear-mile of resurfaced road is credited with 3.5 years of service life, and each linear-mile of repaired road is credited with 1.5 years of service life. As asset manager, you are expected to make repair, resurfacing, and replacement decisions that optimize the use of available funding
Your task is to formulate the above problem as a linear program by specifying (1) the objective function, and (2) all constraint equations. Next, solve the above problem manually or with excel solver, indicating the total miles of roads to be replaced, resurfaced, and repaired, respectively; and the resulting total service years.