Please show your work. Thank you so much for your help!

For a certain company, the cost function for producingxitems isC(x)=40x+150

and the revenue function for sellingx items isR(x)=0.5(x100)^2+5,000. The maximum capacity of the company is130 items.

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!

Part a: Answer the following questions about the cost functionC(x)

and the revenue functionR(x)

.

1. What is the domain and range ofC(x)? Hint: Does calculatingC(x)make sense whenx=10orx=1,000?
2. At what production levelxwill the company receive the most revenue?
3. The maximum revenue occurs whenx=?

Part b: Answer the following questions about the profit functionP(x)

.

1. Assuming that the company sells all that it produces, what is the profit function?
2. P(x)= ?.
3. Hint: Profit = Revenue - Cost
4. The company can choose to produce either60 or70items. What is their profit for each case, and which level of production should they choose?
5. Profit when producing60items =
6. Profit when producing70items =
7. Can you explain, from our model, whythe company makes less profitwhen producing 10 more units?