Question 5: Suppose Duncan only engages in three activities; sleeping, playing Xbox, and working at Starbucks. He has to sleep 8 hours per night and the rest of his time he splits between playing Xbox (X hours per day) and working at Starbucks (S hours per day). He eats ramen noodles (R packages per day) which cost $2 per package. His preferences over playing Xbox and eating ramen noodles are given by 3 the utility function U(X, R) = X0.75 R0 25 (1) Write down Duncan's constrained optimization problem that determines how many hours he will play Xbox (X) and how many packages of ramem noodles he will eat (R). (2) Solve Duncan's problem if he earns $5 an hour at Starbucks. (3) Now, suppose Duncan gets 20$ a day from his parents. Solve Duncan's new problem.
Question 5: Suppose Duncan only engages in three activities; sleeping, playing Xbox, and working at Starbucks. He has to sleep 8 hours per night and the rest of his time he splits between playing Xbox (X hours per day) and working at Starbucks (S hours per day). He eats ramen noodles (R packages per day) which cost $2 per package. His preferences over playing Xbox and eating ramen noodles are given by 3 the utility function U(X, R) = X0.75 R0 25 (1) Write down Duncan's constrained optimization problem that determines how many hours he will play Xbox (X) and how many packages of ramem noodles he will eat (R). (2) Solve Duncan's problem if he earns $5 an hour at Starbucks. (3) Now, suppose Duncan gets 20$ a day from his parents. Solve Duncan's new problem.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Question 5: Suppose Duncan only engages in three activities; sleeping, playing
Xbox, and working at Starbucks. He has to sleep 8 hours per night and the rest of
his time he splits between playing Xbox (X hours per day) and working at Starbucks
(S hours per day). He eats ramen noodles (R packages per day) which cost $2 per
package. His preferences over playing Xbox and eating ramen noodles are given by
3
the utility function
U(X, R) = X0.75R0.25
(1) Write down Duncan's constrained optimization problem that determines how
many hours he will play Xbox (X) and how many packages of ramen noodles
he will eat (R).
(2) Solve Duncan's problem if he earns $5 an hour at Starbucks.
(3) Now, suppose Duncan gets 20$ a day from his parents. Solve Duncan's new
problem.
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