Module Six Discussion Question:

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 the four questions. 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 pastex2you getx2instead, then change yourx2tox^2.

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

For a certain company, the cost function for producingxitems isC(x)=50x+100and the revenue function for sellingxitems isR(x)=0.5(x110)2+6,050. The maximum capacity of the company is130items.

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?

P(x)=

ab

ab

a

|a|

sin(a)

1. .

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

1. What is the domain ofP(x)?

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

1. The company can choose to produce either60or70items. 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?