Chapter 4.5, Problem 40ES

A commercial cattle ranch currently allows $20$ steers per acre of grazing land; on the average its steers weigh $2000\text{ lb}$ at market. Estimates by the Agriculture Department indicate that the average market weight per steer will be reduced by $50\text{ lb}$ for each additional steer added per acre of grazing land. How many steers per acre should be allowed in order for the ranch to get the largest possible total market weight for its cattle?