For a certain company, the cost function for producingxxitems is C(x)=50x+150Cx=50x+150 and the revenue function for sellingxxitems isR(x)=0.5(x110)2+6,050Rx=0.5x1102+6,050. The maximum capacity of the company is 140140items.

The profit function P(x)Pxis the revenue function R(x)Rx(how much it takes in)minus the cost function C(x)Cx(how much it spends). In economic models, one typically assumesthat a company wants to maximize its profit, or at least make a profit!

Answers to some of the questions are given below so that you can check your work.

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

P(x)=??

Hint: Profit = Revenue - Cost as we examined in Discussion 3.

1. What is the domain ofP(x)?

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

1. The company can choose to produce either60 or70items. What is their profit for each case, and which level of production should they choose?

Profit when producing60items =

Profit when producing70items =

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