The Fly-Right Airplane Company builds small jet airplanes to sell to corporationsfor the use of their executives. To meet the needs of these executives, the company's customers sometimes order a custom design of the airplanes being purchased. When thisoccurs, a substantial start-up cost is incurred to initiate the production of these airplanes. Fly-Right has recently received purchase requests from three customers withshort deadlines. However, because the company's production facilities already are almost completely tied up filling previous orders, it will not be able to accept all three orders. Therefore, a decision now needs to be made on the number of airplanes the company will agree to produce (if any) for each of the three customers. The relevant data are given in the following table: Customer 2 Customer 3 Start-up cost Marginal net revenue Customer 1 $ 3 million $ 2 million $2 million $ 3 million $0.8 million 20% Capacity used per plane Maximum order 20% 40% 3 planes 2 planes 2 planes Fly-Right now wants to determine how many airplanes to produce for each customer (if any) to maximize the company's total profit (total net revenue minus start-up costs). 1. Formulate an integer program that maximizes the company's total profit. Define all variables involved clearly, completely and precisely. 2. Solve the problem using Excel solver or any software of your choice. a. Show the initial and optimal tableaus. b. Explain the meaning of the optimal values of the variables involved. c. What is the company's greatest possible total profit?
The Fly-Right Airplane Company builds small jet airplanes to sell to corporationsfor the use of their executives. To meet the needs of these executives, the company's customers sometimes order a custom design of the airplanes being purchased. When thisoccurs, a substantial start-up cost is incurred to initiate the production of these airplanes. Fly-Right has recently received purchase requests from three customers withshort deadlines. However, because the company's production facilities already are almost completely tied up filling previous orders, it will not be able to accept all three orders. Therefore, a decision now needs to be made on the number of airplanes the company will agree to produce (if any) for each of the three customers. The relevant data are given in the following table: Customer 2 Customer 3 Start-up cost Marginal net revenue Customer 1 $ 3 million $ 2 million $2 million $ 3 million $0.8 million 20% Capacity used per plane Maximum order 20% 40% 3 planes 2 planes 2 planes Fly-Right now wants to determine how many airplanes to produce for each customer (if any) to maximize the company's total profit (total net revenue minus start-up costs). 1. Formulate an integer program that maximizes the company's total profit. Define all variables involved clearly, completely and precisely. 2. Solve the problem using Excel solver or any software of your choice. a. Show the initial and optimal tableaus. b. Explain the meaning of the optimal values of the variables involved. c. What is the company's greatest possible total profit?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter7: Nonlinear Optimization Models
Section7.3: Pricing Models
Problem 15P
Related questions
Question
Solving Integer Programming - Number 2 only
Transcribed Image Text:The Fly-Right Airplane Company builds small jet airplanes to sell to corporationsfor the
use of their executives. To meet the needs of these executives, the company's customers
sometimes order a custom design of the airplanes being purchased. When thisoccurs, a
substantial start-up cost is incurred to initiate the production of these airplanes. Fly-Right
has recently received purchase requests from three customers withshort deadlines.
However, because the company's production facilities already are almost completely tied
up filling previous orders, it will not be able to accept all three orders. Therefore, a
decision now needs to be made on the number of airplanes the company will agree to
produce (if any) for each of the three customers. The relevant data are given in the
following table:
Customer
1
$ 3 million
$ 2 million
Customer 2
Customer 3
Start-up cost
Marginal net revenue
$ 2 million
$ 3 million
$ 0.8
million
20%
Capacity used per
plane
Maximum order
Fly-Right now wants to determine how many airplanes to produce for each customer
(if any) to maximize the company's total profit (total net revenue minus start-up costs).
20%
40%
3 planes
2 planes
2 planes
1. Formulate an integer program that maximizes the company's total profit.
Define all variables involved clearly, completely and precisely.
2. Solve the problem using Excel solver or any software of your choice.
a. Show the initial and optimal tableaus.
b. Explain the meaning of the optimal values of the variables involved.
c. What is the company's greatest possible total profit?
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