(20 points) A state highway department is trying to decide whether it should hot-patch a short section of an existing county road or resurface it. If the hot-patch method is used, approximately 300 cubic meters of material would be required at a cost of $700 per cubic meter. Additionally, the shoulders will have to be improved at the same time at a cost of $24,000. These improvements will last 2 years, at which time they will have to be redone. The annual cost of routine maintenance on the patched up road would be $5000. Alternatively, the state can resurface the road at a cost of $850,000. This surface will last 10 years if the road is maintained at a cost of $2000 per year beginning 3 years from now. No matter which alternative is selected, the road will be completely rebuilt in 10 years. At an interest rate of 8% per year, which alternative should the state select on the basis of an annual worth analysis? Please show work, Thank You.