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 paste x2 you get x2 instead, then change your x2 to x^2. Hint: This question is an extension to the topic of Discussion Three. For a certain company, the cost function for producing x items is C(x)=50x+150 and the revenue function for selling x items is R(x)=−0.5(x−130)^2+8,450. The maximum capacity of the company is 190 items. The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that 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 function C(x) and the revenue function R(x). What is the domain and range of C(x)? Hint: Does calculating C(x) make sense when x=−10 or x=1,000? What is the meaning of the slope and intercept of C(x)? Hint: Review the Models and Applications reading from Module One. At what production level x will the company receive the most revenue? The maximum revenue occurs when x= . Hint: Look at the graph of a parabola.
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 paste x2 you get x2 instead, then change your x2 to x^2.
Hint: This question is an extension to the topic of Discussion Three.
For a certain company, the cost function for producing x items is C(x)=50x+150 and the revenue function for selling x items is R(x)=−0.5(x−130)^2+8,450. The maximum capacity of the company is 190 items.
The profit function P(x) is the revenue function R(x) (how much it takes in) minus the cost function C(x) (how much it spends). In economic models, one typically assumes that 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 function C(x) and the revenue function R(x).
- What is the domain and range of C(x)?
Hint: Does calculating C(x) make sense when x=−10 or x=1,000?
- What is the meaning of the slope and intercept of C(x)?
Hint: Review the Models and Applications reading from Module One.
- At what production level x will the company receive the most revenue?
The maximum revenue occurs when x= .
Hint: Look at the graph of a parabola.
Part b: Answer the following questions about the profit function P(x).
- Assuming that the company sells all that it produces, what is the profit function?
P(x)= .
Hint: Profit = Revenue - Cost as we already discussed in Discussion 3.
- Why is finding the range of P(x) important?
- The company can choose to produce either 80 or 90 items. What is their profit for each case, and which level of production should they choose?
Profit when producing 80 items =
Profit when producing 90 items =
- Can you explain, from our model, why the company makes less profit when producing 10 more units?
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