Please help and explain your process please!

For a certain company, the cost function for producingxitems isC(x)=40x+250and the revenue function for sellingxitems isR(x)=0.5(x80)^2

+3,200. The maximum capacity of the company is110items.

The profit functionP(x)is the revenue functionR(x) (how much it takes in)minus the cost functionC(x)(how much it spends). In economic models, one typically assumesthat a company wants to maximize its profit, or at least make a profit!

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

P(x)=

2.) What is the domain ofP(x)?

Hint: Does calculatingP(x)make sense whenx=10orx=1,000?

3.) The company can choose to produce either40or50items. What is their profit for each case, and which level of production should they choose?

Profit when producing40items =

Profit when producing50items =

4.) Can you explain, from our model, whythe company makes less profitwhen producing 10 more units?