For a certain company, the cost function for producingx

items isC(x)=50x+250

and the revenue function for sellingx

items isR(x)=0.5(x130)2 +8,450. The maximum capacity of the company is180items.

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 either80 or90

items. What is their profit for each case, and which level of production should they choose? Profit when producing80 items =????

Profit when producing90 items =???

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