PIM Industries Incorporated manufactures electronics components. Each unit costs $$40$ before the final test. The final test rejects, on average, $5\%$ of the $50,000$ units manufactured per year. The average rejection rate of the industry is $3\%.$ A consultant has determined that poor lighting is the most likely cause of this high rejection rate. It would cost $$125,000$ to install adequate lighting in the assembly department, which would be useful for $5$ years. With adequate lighting $($which will cost an additional $$5,500$ of operating costs per year$),$ the firm expects to reduce its rejection rate to no higher than the industry average.