For a certain company, the cost function for producing x items is C(x)=50x+200 and the revenue function for selling x items is R(x)=−0.5(x−100)2+5,000. The maximum capacity of the company is 120 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! 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 50 or 60 items. What is their profit for each case, and which level of production should they choose? Profit when producing 50 items = Profit when producing 60 items = Can you explain, from our model, why the company makes less profit when producing 10 more units?
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.
For a certain company, the cost function for producing x items is C(x)=50x+200 and the revenue function for selling x items is R(x)=−0.5(x−100)2+5,000. The maximum capacity of the company is 120 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!
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 50 or 60 items. What is their profit for each case, and which level of production should they choose?
Profit when producing 50 items =
Profit when producing 60 items =
- Can you explain, from our model, why the company makes less profit when producing 10 more units?
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