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Question: The net monthly profit in dollars from the sale of gourmet popcorn is described by the function: P (n) = 80ne 0.1 + 60, n ≥ 2 Where: P(n) represents the net profit in dollars n is the number of gourmet popcorn bags sold in hundreds. a. The company has the capacity to produce up to 800 bags of gourmet popcorn per month. Determine the number of popcorn bags that should be sold to maximize the monthly profit. What is the maximum profit in dollars? b. Find the number of bags of popcorn (in hundreds) the company should produce to achieve the highest profit, up to their capacity of 1700 bags per month. Then, determine whether this profit point is an absolute maximum or a local maximum, using calculus terminology. c. Find the number of bags of gourmet popcorn (in hundreds) that the company must sell in order to achieve a marginal profit of $0.56 per unit. If the profit function never achieves this marginal profit, explain why not.

Question: The net monthly profit in dollars from the sale of gourmet popcorn is described by the function: P (n) = 80ne 0.1 + 60, n ≥ 2 Where: P(n) represents the net profit in dollars n is the number of gourmet popcorn bags sold in hundreds. a. The company has the capacity to produce up to 800 bags of gourmet popcorn per month. Determine the number of popcorn bags that should be sold to maximize the monthly profit. What is the maximum profit in dollars? b. Find the number of bags of popcorn (in hundreds) the company should produce to achieve the highest profit, up to their capacity of 1700 bags per month. Then, determine whether this profit point is an absolute maximum or a local maximum, using calculus terminology. c. Find the number of bags of gourmet popcorn (in hundreds) that the company must sell in order to achieve a marginal profit of $0.56 per unit. If the profit function never achieves this marginal profit, explain why not.

Elementary Algebra
Elementary Algebra
17th Edition
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:Lynn Marecek, MaryAnne Anthony-Smith
Chapter10: Quadratic Equations
Section10.4: Solve Applications Modeled By Quadratic Equations
Problem 159E: A bullet is fired straight up from a BB gun with initial velocity 1120 feet per second at an initial...
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Solve this problem and provide a detailed explanation with full mathematical steps and reasoning shown. If there are any problems with the question provide an explanation accordingly.

Question: The net monthly profit in dollars from the sale of gourmet popcorn is described by the function: P (n) = 80ne 0.1 + 60, n ≥ 2 Where: P(n) represents the net profit in dollars n is the number of gourmet popcorn bags sold in hundreds. a. The company has the capacity to produce up to 800 bags of gourmet popcorn per month. Determine the number of popcorn bags that should be sold to maximize the monthly profit. What is the maximum profit in dollars? b. Find the number of bags of popcorn (in hundreds) the company should produce to achieve the highest profit, up to their capacity of 1700 bags per month. Then, determine whether this profit point is an absolute maximum or a local maximum, using calculus terminology. c. Find the number of bags of gourmet popcorn (in hundreds) that the company must sell in order to achieve a marginal profit of $0.56 per unit. If the profit function never achieves this marginal profit, explain why not.
Transcribed Image Text:Question: The net monthly profit in dollars from the sale of gourmet popcorn is described by the function: P (n) = 80ne 0.1 + 60, n ≥ 2 Where: P(n) represents the net profit in dollars n is the number of gourmet popcorn bags sold in hundreds. a. The company has the capacity to produce up to 800 bags of gourmet popcorn per month. Determine the number of popcorn bags that should be sold to maximize the monthly profit. What is the maximum profit in dollars? b. Find the number of bags of popcorn (in hundreds) the company should produce to achieve the highest profit, up to their capacity of 1700 bags per month. Then, determine whether this profit point is an absolute maximum or a local maximum, using calculus terminology. c. Find the number of bags of gourmet popcorn (in hundreds) that the company must sell in order to achieve a marginal profit of $0.56 per unit. If the profit function never achieves this marginal profit, explain why not.
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