I have problems with these types of questions.
A manufacturer finds it costs him x² + 5x + 7 dollars to produce x tons of an item. At production levels above 3 tons, he must hire additional workers, and his costs increase by 3(x - 3) dollars on his total production. The price he receives is $13 per ton regardless of how much he manufacturers and if he has a plant capacity of 10 tons.
a) What is the domain of the profit function?
b) Write the profit function for a production level below 3 tons.
c) Write the profit function for a production level above 3 tons.
d) What level of output maximmizes profits? Justify your answer.
so the cost function is C(x) = x² + 5x + 7 if below 3 tons, but (x² + 5x + 7)3(x - 3) if above 3 tons? And I'm not even sure what the last part is saying, it just throws me off.