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Profit The profit P (in dollars) made by a cinema from selling & Bags of popc x² 28,000 3,300, 0≤x≤ 50,000. (a) Find the intervals on which P is increasing and decreasing. (Enter your answers using interval notation.) P = 2.34x- increasing modeled by decreasing (b) If you owned the cinema, what price would you charge to obtain a maximum profit for popcorn? Explain your reasoning. You should charge the price that yields sales of x = 32,760 bags of popcorn. Since the function changes from increasing to decreasing at x = 32,760, the maximum profit occurs at this value. O You should charge the price that yields sales of x= 32,260 bags of popcorn. Since the function changes from increasing to decreasing at x = 32,260, the minimum profit occurs at this value. O You should charge the price that yields sales of x = 32,760 bags of popcorn. Since the function changes from decreasing to increasing at x = 32,760, the minimum profit occurs at this value. O You should charge the price that yields sales of x= 33,260 bags of popcorn. Since the function changes from decreasing to increasing at x = 33,260, the maximum profit occurs at this value. O You should charge the price that yields sales of x= 32,660 bags of popcorn. Since the function changes from decreasing to increasing at x = 32,660, the minimum profit occurs at this value.

Profit The profit P (in dollars) made by a cinema from selling & Bags of popc x² 28,000 3,300, 0≤x≤ 50,000. (a) Find the intervals on which P is increasing and decreasing. (Enter your answers using interval notation.) P = 2.34x- increasing modeled by decreasing (b) If you owned the cinema, what price would you charge to obtain a maximum profit for popcorn? Explain your reasoning. You should charge the price that yields sales of x = 32,760 bags of popcorn. Since the function changes from increasing to decreasing at x = 32,760, the maximum profit occurs at this value. O You should charge the price that yields sales of x= 32,260 bags of popcorn. Since the function changes from increasing to decreasing at x = 32,260, the minimum profit occurs at this value. O You should charge the price that yields sales of x = 32,760 bags of popcorn. Since the function changes from decreasing to increasing at x = 32,760, the minimum profit occurs at this value. O You should charge the price that yields sales of x= 33,260 bags of popcorn. Since the function changes from decreasing to increasing at x = 33,260, the maximum profit occurs at this value. O You should charge the price that yields sales of x= 32,660 bags of popcorn. Since the function changes from decreasing to increasing at x = 32,660, the minimum profit occurs at this value.

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.1: Quadratic Functions And Models
Problem 58E: Agriculture At a certain vineyard it is found that each grape vine produces about 10 lb of grapes in...
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Profit The profit P (in dollars) made by a cinema from selling x bags of popcorn can be modeled by x² 28,000 - 3,300, 0≤x≤ 50,000. (a) Find the intervals on which P is increasing and decreasing. (Enter your answers using interval notation.) P= 2.34x- increasing decreasing (b) If you owned the cinema, what price would you charge to obtain a maximum profit for popcorn? Explain your reasoning. O You should charge the price that yields sales of x = 32,760 bags of popcorn. Since the function changes from increasing to decreasing at x = 32,760, the maximum profit occurs at this value. O You should charge the price that yields sales of x = 32,260 bags of popcorn. Since the function changes from increasing to decreasing at x = 32,260, the minimum profit occurs at this value. O You should charge the price that yields sales of x = 32,760 bags of popcorn. Since the function changes from decreasing to increasing at x = 32,760, the minimum profit occurs at this value. O You should charge the price that yields sales of x = 33,260 bags of popcorn. Since the function changes from decreasing to increasing at x = 33,260, the maximum profit occurs at this value. O You should charge the price that yields sales of x = 32,660 bags of popcorn. Since the function changes from decreasing to increasing at x = 32,660, the minimum profit occurs at this value.
Transcribed Image Text:Profit The profit P (in dollars) made by a cinema from selling x bags of popcorn can be modeled by x² 28,000 - 3,300, 0≤x≤ 50,000. (a) Find the intervals on which P is increasing and decreasing. (Enter your answers using interval notation.) P= 2.34x- increasing decreasing (b) If you owned the cinema, what price would you charge to obtain a maximum profit for popcorn? Explain your reasoning. O You should charge the price that yields sales of x = 32,760 bags of popcorn. Since the function changes from increasing to decreasing at x = 32,760, the maximum profit occurs at this value. O You should charge the price that yields sales of x = 32,260 bags of popcorn. Since the function changes from increasing to decreasing at x = 32,260, the minimum profit occurs at this value. O You should charge the price that yields sales of x = 32,760 bags of popcorn. Since the function changes from decreasing to increasing at x = 32,760, the minimum profit occurs at this value. O You should charge the price that yields sales of x = 33,260 bags of popcorn. Since the function changes from decreasing to increasing at x = 33,260, the maximum profit occurs at this value. O You should charge the price that yields sales of x = 32,660 bags of popcorn. Since the function changes from decreasing to increasing at x = 32,660, the minimum profit occurs at this value.
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