Pricing In The Cost Of Pollution

Calculus Level 2

Under the Kyoto Protocol, each country is assigned a quota on the amount of greenhouse gases which it emits a year. In turn, these countries set quotas on the emissions produced by local businesses and organizations. Each operator has an allowance of carbon credits, and may choose to purchase additional carbon credits as required.

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?

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