Part 1: The boat has a capacity of 200 guests. Currently, 4-hour cruises around Manhattan (with...
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Part 1: The boat has a capacity of 200 guests. Currently, 4-hour cruises around Manhattan (with dinner) cost $175 per person with a minimum of 100 people. For groups greater than 125, there is a discount following the table: NUMBER OF GUESTS 101 - 125 126-150 151 - 175 176-200 PRICE PER GUEST $175 $162.50 $150 $137.50 Under these conditions what size group will maximize revenue? If the Price function were written using the given prices above, what type of function would it actually be? For purposes of this problem, the Price function will be approximated as a linear function where we assume for each additional guest the price will drop by $0.50, since for each additional 25 guests the price drops $12.50 which would be an average rate of change of $0.50. Let x be the number of guests and write a linear price function, P(x) using this assumption. What is the practical domain for x? Write the Revenue function, R(x), using P(x), where Revenue = price * demand. What type of function is the Revenue function? Explain using complete sentences. Use the First Derivative Test to determine the optimum number of passengers. Show all supporting work, interpret the solution as a complete sentence. Give the number of passengers, price charged, and the total revenue in your final answer. Part 1: The boat has a capacity of 200 guests. Currently, 4-hour cruises around Manhattan (with dinner) cost $175 per person with a minimum of 100 people. For groups greater than 125, there is a discount following the table: NUMBER OF GUESTS 101 - 125 126-150 151 - 175 176-200 PRICE PER GUEST $175 $162.50 $150 $137.50 Under these conditions what size group will maximize revenue? If the Price function were written using the given prices above, what type of function would it actually be? For purposes of this problem, the Price function will be approximated as a linear function where we assume for each additional guest the price will drop by $0.50, since for each additional 25 guests the price drops $12.50 which would be an average rate of change of $0.50. Let x be the number of guests and write a linear price function, P(x) using this assumption. What is the practical domain for x? Write the Revenue function, R(x), using P(x), where Revenue = price * demand. What type of function is the Revenue function? Explain using complete sentences. Use the First Derivative Test to determine the optimum number of passengers. Show all supporting work, interpret the solution as a complete sentence. Give the number of passengers, price charged, and the total revenue in your final answer.
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Related Book For
Fundamental Managerial Accounting Concepts
ISBN: 978-0078025655
7th edition
Authors: Thomas Edmonds, Christopher Edmonds, Bor Yi Tsay, Philip Old
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