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The Fallwing family loves gummy bears and pickled strawberries. Their monthly GB/PS utility function is given by U(x, y) = 13lnx + 7lny, where x = the number of pounds of gummy bears and y = the number of pounds of pickled strawberries that they consume each month. (a) Find the quantities of gummy bears and pickled strawberries that the Fallwin family should consume to maximize their GB/PS utility, given that gummy bears cost $8.00/pound, pickled strawberries cost $6.00/pound, and the Fallwing's monthly GB/PS budget is $480.00. What is their maximum monthly GB/PS utility? (b) Show how you know that the GB/PS utility that you found in (a) is the Fallwing's absolute maximum.

The Fallwing family loves gummy bears and pickled strawberries. Their monthly GB/PS utility function is given by U(x, y) = 13lnx + 7lny, where x = the number of pounds of gummy bears and y = the number of pounds of pickled strawberries that they consume each month. (a) Find the quantities of gummy bears and pickled strawberries that the Fallwin family should consume to maximize their GB/PS utility, given that gummy bears cost $8.00/pound, pickled strawberries cost $6.00/pound, and the Fallwing's monthly GB/PS budget is $480.00. What is their maximum monthly GB/PS utility? (b) Show how you know that the GB/PS utility that you found in (a) is the Fallwing's absolute maximum.

Advanced Engineering Mathematics
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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The Fallwing family loves gummy bears and pickled strawberries. Their monthly GB/PS utility function is given by U(x, y) = 13lnx + 7lny, where x = the number of pounds of gummy bears and y = the number of pounds of pickled strawberries that they consume each month. (a) Find the quantities of gummy bears and pickled strawberries that the Fallwin family should consume to maximize their GB/PS utility, given that gummy bears cost $8.00/pound, pickled strawberries cost $6.00/pound, and the Fallwing's monthly GB/PS budget is $480.00. What is their maximum monthly GB/PS utility? (b) Show how you know that the GB/PS utility that you found in (a) is the Fallwing's absolute maximum.
Transcribed Image Text:The Fallwing family loves gummy bears and pickled strawberries. Their monthly GB/PS utility function is given by U(x, y) = 13lnx + 7lny, where x = the number of pounds of gummy bears and y = the number of pounds of pickled strawberries that they consume each month. (a) Find the quantities of gummy bears and pickled strawberries that the Fallwin family should consume to maximize their GB/PS utility, given that gummy bears cost $8.00/pound, pickled strawberries cost $6.00/pound, and the Fallwing's monthly GB/PS budget is $480.00. What is their maximum monthly GB/PS utility? (b) Show how you know that the GB/PS utility that you found in (a) is the Fallwing's absolute maximum.
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