For a certain company, the cost function for producing x items is C(x)=40x+250
and the revenue function for selling x items is R(x)=−0.5(x−100)^2+5,000.
The maximum capacity of the company is 150 items.

1.Assuming that the company sells all that it produces, what is the profit function?
P(x)=

2.What is the domain of P(x)?

3.The company can choose to produce either 60 or 70 items. What is their profit for each case, and which level of production should they choose?
Profit when producing 60 items =
Profit when producing 70 items =

4.Can you explain, from our model, why the company makes less profit when producing 10 more units?

Please show detailed work for each question.