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Coastal Soda Sales has been granted exclusive market rights to the upcoming Beaufort Seafood Festival. This means that during the festival Coastal will have a monopoly, and it is anxious to take advantage of this position in its pricing strategy. The daily demand function is p = 2 - 0.0004x and the daily total cost function is C(x) = 500 + 0.2x + 0.0001x² where x is the number of units. (a) Determine Coastal's total revenue, R(x), and profit functions, P(x), in dollars. R(x) = P(x) = (b) What profit-maximizing price per soda should Coastal charge? per soda How many sodas per day would it expect to sell at this price? sodas per day What would be the daily profits? $ per day (c) If the festival organizers wanted to set an economically efficient price of $1.25 per soda, how would this change the results from part (b)? (Round your answer for daily profits to the nearest cent.) sodas per day it would expect to sell sodas per day daily profits $ per day Would Coastal be willing to provide sodas for the festival at this regulated price? Why or why not? O Yes, Coastal would still provide sodas, because the profits would be significantly greater. O Yes, Coastal would still provide sodas, because the profits would be almost the same. O No, Coastal would no longer provide sodas, because the profits would be significantly less.

Coastal Soda Sales has been granted exclusive market rights to the upcoming Beaufort Seafood Festival. This means that during the festival Coastal will have a monopoly, and it is anxious to take advantage of this position in its pricing strategy. The daily demand function is p = 2 - 0.0004x and the daily total cost function is C(x) = 500 + 0.2x + 0.0001x² where x is the number of units. (a) Determine Coastal's total revenue, R(x), and profit functions, P(x), in dollars. R(x) = P(x) = (b) What profit-maximizing price per soda should Coastal charge? per soda How many sodas per day would it expect to sell at this price? sodas per day What would be the daily profits? $ per day (c) If the festival organizers wanted to set an economically efficient price of $1.25 per soda, how would this change the results from part (b)? (Round your answer for daily profits to the nearest cent.) sodas per day it would expect to sell sodas per day daily profits $ per day Would Coastal be willing to provide sodas for the festival at this regulated price? Why or why not? O Yes, Coastal would still provide sodas, because the profits would be significantly greater. O Yes, Coastal would still provide sodas, because the profits would be almost the same. O No, Coastal would no longer provide sodas, because the profits would be significantly less.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.8: Linear Programming
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Coastal Soda Sales has been granted exclusive market rights to the upcoming Beaufort Seafood Festival. This means that during the festival Coastal will have a monopoly, and it is anxious to take advantage of this position in its pricing strategy. The daily demand function is p = 2 – 0.0004x and the daily total cost function is C(x) = 500 + 0.2x + 0.0001x² where x is the number of units. (a) Determine Coastal's total revenue, R(x), and profit functions, P(x), in dollars. R(x) P(x) (b) What profit-maximizing price per soda should Coastal charge? $ per soda How many sodas per day would it expect to sell at this price? sodas per day What would be the daily profits? $ per day (c) If the festival organizers wanted to set an economically efficient price of $1.25 per soda, how would this change the results from part (b)? (Round your answer for daily profits to the nearest cent.) sodas per day it would expect to sell sodas per day daily profits per day Would Coastal be willing to provide sodas for the festival at this regulated price? Why or why not? Yes, Coastal would still provide sodas, because the profits would be significantly greater. Yes, Coastal would still provide sodas, because the profits would be almost the same. No, Coastal would no longer provide sodas, because the profits would be significantly less.
Transcribed Image Text:Coastal Soda Sales has been granted exclusive market rights to the upcoming Beaufort Seafood Festival. This means that during the festival Coastal will have a monopoly, and it is anxious to take advantage of this position in its pricing strategy. The daily demand function is p = 2 – 0.0004x and the daily total cost function is C(x) = 500 + 0.2x + 0.0001x² where x is the number of units. (a) Determine Coastal's total revenue, R(x), and profit functions, P(x), in dollars. R(x) P(x) (b) What profit-maximizing price per soda should Coastal charge? $ per soda How many sodas per day would it expect to sell at this price? sodas per day What would be the daily profits? $ per day (c) If the festival organizers wanted to set an economically efficient price of $1.25 per soda, how would this change the results from part (b)? (Round your answer for daily profits to the nearest cent.) sodas per day it would expect to sell sodas per day daily profits per day Would Coastal be willing to provide sodas for the festival at this regulated price? Why or why not? Yes, Coastal would still provide sodas, because the profits would be significantly greater. Yes, Coastal would still provide sodas, because the profits would be almost the same. No, Coastal would no longer provide sodas, because the profits would be significantly less.
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