Angelina is thinking of investing $175,800$ in a new plant which can be built and become operational immediately. The plant will generate revenues of $30,000$ per year for as long as she maintains it$.$ The maintenance cost will start at $6,000$ per year and will increase $5\%$ per year thereafter. Angelina intends to run the plant as long as the cash generated exceeds the maintenance costs. The interest rate is $8\%$ per year. Assuming that all revenue and maintenance costs occur at the end of the year, should Angelina invest in the plant?