Pricing In The Cost Of Pollution
Caterpillar Inc. runs an industrial facility which produces tractors. They know that if they produce \(T\) tractors a month, their net profit from production would be \( ( - T^2 + 50T - 200) \) thousand dollars. However, if they produce more than 10 tractors, then each additional tractor will cost them ten thousand dollars in carbon credits.
What is the optimal number of tractors which Caterpillar should produce, in order to maximize their profit?