5. An app developer has been offered a contract by a large international bank to design some software. The developer will receive a basic payment of $1 million, but there is also the possibility of a bonus payment B. The bonus payment will only be paid if the developer completes the work within the term of the contract, T months. The developer is allowed to decide in advance the number of months, T, the project will take to complete. The bonus, B, is related to T by B = 1 T5' working in units of $ million. The developer is uncertain how long the project will take to complete and decides to assume that completion time, C, is a uniform random variable on the interval [1,2] (i.e. that the project will take at least one month, but not more than 2 months to complete). (a) What is the expected total payment the developer will receive in terms of T? (b) Even though the developer is uncertain about the completion time, the contract states a particular time must be chosen before work begins. Assume that the developer choose a value for T in the interval [1,2]. What particular value for T should the developer select to maximise expected total payment?
5. An app developer has been offered a contract by a large international bank to design some software. The developer will receive a basic payment of $1 million, but there is also the possibility of a bonus payment B. The bonus payment will only be paid if the developer completes the work within the term of the contract, T months. The developer is allowed to decide in advance the number of months, T, the project will take to complete. The bonus, B, is related to T by B = 1 T5' working in units of $ million. The developer is uncertain how long the project will take to complete and decides to assume that completion time, C, is a uniform random variable on the interval [1,2] (i.e. that the project will take at least one month, but not more than 2 months to complete). (a) What is the expected total payment the developer will receive in terms of T? (b) Even though the developer is uncertain about the completion time, the contract states a particular time must be chosen before work begins. Assume that the developer choose a value for T in the interval [1,2]. What particular value for T should the developer select to maximise expected total payment?
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 21P
Related questions
Question
![5. An app developer has been offered a contract by a large international bank to design
some software. The developer will receive a basic payment of $1 million, but there is
also the possibility of a bonus payment B.
The bonus payment will only be paid if the developer completes the work within the
term of the contract, T months. The developer is allowed to decide in advance the
number of months, T, the project will take to complete. The bonus, B, is related to T
by
B
=
1
T5'
working in units of $ million. The developer is uncertain how long the project will take to
complete and decides to assume that completion time, C, is a uniform random variable
on the interval [1,2] (i.e. that the project will take at least one month, but not more
than 2 months to complete).
(a) What is the expected total payment the developer will receive in terms of T?
(b) Even though the developer is uncertain about the completion time, the contract
states a particular time must be chosen before work begins. Assume that the
developer choose a value for T in the interval [1,2]. What particular value for T
should the developer select to maximise expected total payment?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69cce4ac-4bf6-4e6b-8636-bf160e045b58%2F9b37e227-e945-41cf-b1d7-19374b343623%2F4za2t5p_processed.jpeg&w=3840&q=75)
Transcribed Image Text:5. An app developer has been offered a contract by a large international bank to design
some software. The developer will receive a basic payment of $1 million, but there is
also the possibility of a bonus payment B.
The bonus payment will only be paid if the developer completes the work within the
term of the contract, T months. The developer is allowed to decide in advance the
number of months, T, the project will take to complete. The bonus, B, is related to T
by
B
=
1
T5'
working in units of $ million. The developer is uncertain how long the project will take to
complete and decides to assume that completion time, C, is a uniform random variable
on the interval [1,2] (i.e. that the project will take at least one month, but not more
than 2 months to complete).
(a) What is the expected total payment the developer will receive in terms of T?
(b) Even though the developer is uncertain about the completion time, the contract
states a particular time must be chosen before work begins. Assume that the
developer choose a value for T in the interval [1,2]. What particular value for T
should the developer select to maximise expected total payment?
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 1 images
Recommended textbooks for you
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,