Suppose Paul's Utility Depends on the Amount of Time Spent

question 47

Essay

Suppose Paul's utility depends on the amount of time spent playing on the Internet (x)and the amount of time playing video games (y),and his utility function is
U(x,y)= 3x⁰.² y⁰.⁸
He has 15 hours of free time to spend on these two activities each week,and his goal is to maximize his utility.
a.Set up the Lagrangian for this constrained maximization problem.
b.What are the necessary conditions for the optimum from the Lagrangian?
c.What is the optimal amount of time spent surfing the Internet and playing video games each week?

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Definitions:

Connective Tissues

Tissues in the body that support, bind together, or separate other tissues and organs, characterized by few cells and substantial extracellular matrix.

Bone and Cartilage

Connective tissues in the body, where bone is hard and dense, providing structure and support, while cartilage is more flexible and cushions joints.

Lacunae

Small cavities in bone or cartilage tissue housing cells like osteocytes or chondrocytes.

Simple Squamous Epithelium

A single layer of flat cells lining surfaces where diffusion or filtration occurs, such as the alveoli in the lungs.