Solve the problem below. For your initial post in Brightspace, copy the description of your company given in the box below and then enter your solution to all seven questions (questions 1 through 7) of the problem. To copy the description of your company, highlighting and using "copy" from here in Mobius and then using "paste" into Brightspace should work.However, if when you copy and pastex

2

you getx2

instead, then change yourx2

tox^2

.

Hint: This question is an extension to the topic of Discussion Three.

For a certain company, the cost function for producingx

items isC(x)=50x+200

and the revenue function for sellingx

items isR(x)=0.5(x120)^2+7,200

. The maximum capacity of the company is170

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.

Part a: Answer the following questions about the cost functionC(x)

and the revenue functionR(x)

.

1. What is the domain and range ofC(x) ?
2. Hint: Does calculatingC(x)
3. make sense whenx=10orx=1,000
4. What is the meaning of the slope and intercept ofC(x)
5. At what production levelx will the company receive the most revenue?
6. The maximum revenue occurs whenx=

Part b: Answer the following questions about the profit functionP(x)

.

1. Assuming that the company sells all that it produces, what is the profit function?
2. P(x)=
3. Why is finding the range ofP(x)important?
4. The company can choose to produce either70or80
5. items. What is their profit for each case, and which level of production should they choose?
6. Profit when producing70
7. items =
8. Profit when producing80
9. items =
10. Can you explain, from our model, whythe company makes less profitwhen producing 10 more units?