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For a certain company, the cost function for producing æ items is C (x) = 30 x + 100 and the revenue function for selling æ items is R(x) = -0.5(x – 80)2 + 3,200. The maximum capacity of | the company is 130 items. he profit function P(x) is the revenue function R (x) (how much it takes in) minus the cost function (x) (how much it spends). In economic models, one typically assumes that a company wants to haximize its profit, or at least make a profit! nswers 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) = 国团. Hint: Profit = Revenue - Cost as we examined in Discussion 3. 2. What is the domain of P(x)? Hint: Does calculating P(x) make sense when æ = -10 or æ = 1,000? 3. 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 = Number Profit when producing 60 items = Number 4. Can you explain, from our model, why the company makes less profit when producing 10 more units?

For a certain company, the cost function for producing æ items is C (x) = 30 x + 100 and the revenue function for selling æ items is R(x) = -0.5(x – 80)2 + 3,200. The maximum capacity of | the company is 130 items. he profit function P(x) is the revenue function R (x) (how much it takes in) minus the cost function (x) (how much it spends). In economic models, one typically assumes that a company wants to haximize its profit, or at least make a profit! nswers 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) = 国团. Hint: Profit = Revenue - Cost as we examined in Discussion 3. 2. What is the domain of P(x)? Hint: Does calculating P(x) make sense when æ = -10 or æ = 1,000? 3. 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 = Number Profit when producing 60 items = Number 4. Can you explain, from our model, why the company makes less profit when producing 10 more units?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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For a certain company, the cost function for producing a items is C (x) = 30 x + 100 and the revenue function for selling x items is R(x) = -0.5(x – 80)2 + 3,200. The maximum capacity of the company is 130 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. 1. Assuming that the company sells all that it produces, what is the profit function? P(x) = 固岛。 Hint: Profit = Revenue - Cost as we examined in Discussion 3. 2. What is the domain of P (x)? Hint: Does calculating P (x) make sense when x = -10 or x = 1,000? 3. 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 = Number Profit when producing 60 items = Number 4. Can you explain, from our model, why the company makes less profit when producing 10 more units?
Transcribed Image Text:For a certain company, the cost function for producing a items is C (x) = 30 x + 100 and the revenue function for selling x items is R(x) = -0.5(x – 80)2 + 3,200. The maximum capacity of the company is 130 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. 1. Assuming that the company sells all that it produces, what is the profit function? P(x) = 固岛。 Hint: Profit = Revenue - Cost as we examined in Discussion 3. 2. What is the domain of P (x)? Hint: Does calculating P (x) make sense when x = -10 or x = 1,000? 3. 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 = Number Profit when producing 60 items = Number 4. Can you explain, from our model, why the company makes less profit when producing 10 more units?
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