For a certain company, the cost function for producing x items is C (x) = 30x + 150 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 140 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!

1: What is the domain and range of C (x)?

2: What is the meaning of the slope and intercept of C (x)?

3: At what production level x will the company receive the most revenue? The maximum revenue occurs when x= ?

4: Assuming that the company sells all that it produces, what is the profit function?

5: The company can choose to produce either 70 or 80 items. What is their profit for each case?