For a certain company, the cost function for producingx

items isC(x)=30x+100

and the revenue function for sellingx

items isR(x)=0.5(x100)

2

+5,000

. The maximum capacity of the company is160

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!

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?
2. P(x)=

1. Hint: Profit = Revenue - Cost as we examined in Discussion 3.
2. What is the domain ofP(x)
3. Hint: Does calculatingP(x)
4. make sense whenx=10
5. orx=1,000
6. ?
7. The company can choose to produce either70
8. or80
9. items. What is their profit for each case, and which level of production should they choose?
10. Profit when producing70
11. items =
12. Profit when producing80
13. items =
14. Can you explain, from our model, whythe company makes less profitwhen producing 10 more units?