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a. Formulate the linear program that represents this problem and solve it. For the purposes of this exercise you can assume that is possible to buy fractions of a boat, no need to make the variables integer. b. What is the optimal solution (purchase plan)? How many of each container should be purchased, and what should the resultant cost be? c. Suppose that the requirement of at least 660 for seating capacity is reduced to 650. Without resolving the problem, can you determine how this would change the optimal solution? What would be the new cost?

a. Formulate the linear program that represents this problem and solve it. For the purposes of this exercise you can assume that is possible to buy fractions of a boat, no need to make the variables integer. b. What is the optimal solution (purchase plan)? How many of each container should be purchased, and what should the resultant cost be? c. Suppose that the requirement of at least 660 for seating capacity is reduced to 650. Without resolving the problem, can you determine how this would change the optimal solution? What would be the new cost?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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A shipping company is planning on purchasing three different types of boats: A, B and C. The relevant data is summarized in the following table: Cost (million $) per unit Seating capacity Expected profit ($) per unit A 6.5 • At most 12 boats in all. B 7.8 45 150,000 60 75 175,000 218,000 The objective is to minimize the expansion costs under the following restrictions: • Required returns: $1,800,000. • Required seating capacity: at least 660. • At most 8 type C boats may be purchased C 9.2 a. Formulate the linear program that represents this problem and solve it. For the purposes of this exercise you can assume that is possible to buy fractions of a boat, no need to make the variables integer. b. What is the optimal solution (purchase plan)? How many of each container should be purchased, and what should the resultant cost be? c. Suppose that the requirement of at least 660 for seating capacity is reduced to 650. Without resolving the problem, can you determine how this would change the optimal solution? What would be the new cost? Solve it using Simplex method, do not use any software.Show your work.
Transcribed Image Text:A shipping company is planning on purchasing three different types of boats: A, B and C. The relevant data is summarized in the following table: Cost (million $) per unit Seating capacity Expected profit ($) per unit A 6.5 • At most 12 boats in all. B 7.8 45 150,000 60 75 175,000 218,000 The objective is to minimize the expansion costs under the following restrictions: • Required returns: $1,800,000. • Required seating capacity: at least 660. • At most 8 type C boats may be purchased C 9.2 a. Formulate the linear program that represents this problem and solve it. For the purposes of this exercise you can assume that is possible to buy fractions of a boat, no need to make the variables integer. b. What is the optimal solution (purchase plan)? How many of each container should be purchased, and what should the resultant cost be? c. Suppose that the requirement of at least 660 for seating capacity is reduced to 650. Without resolving the problem, can you determine how this would change the optimal solution? What would be the new cost? Solve it using Simplex method, do not use any software.Show your work.
Expert Solution
Step 1: Introduce the question:

For this question, I will formulate the Linear programming model, and then, I will solve this LP using the 2 phase simplex method, There are a total of three decision variables and it is a cost minimization problem, from the REF of the last table, I can answer the rest questions, 

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