For a certain company, the cost function for producingx

items isC(x)=40x+250

and the revenue function for sellingx

items isR(x)=0.5(x90)^2 + 4,050. The maximum capacity of the company is120

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

P(x)=

2:What is the domain ofP(x)?

3:The company can choose to produce either50or60items. What is their profit for each case, and which level of production should they choose?

Profit when producing50 items =

Profit when producing60items =

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