**Problem Statement:**Robinson is trapped on an island and can produce Fish (F) or Coconuts (C) with his time. Let $L_F$ and $L_C$ denote labor hours dedicated to fishing or gathering coconuts, respectively.Robinson's technological relationships for producing fish is given by:\[ F = \frac{1}{2} \sqrt{L_F} \]Robinson's technological relationships for producing coconuts is given by:\[ C = \frac{1}{4} \sqrt{L_C} \]Which of the following correctly expresses the relationship between fish and coconuts along Robinson's PPF for a single 24 hour day (assume he doesn't sleep)?**Options:**- $ F^2 + 4C^2 = 6 $- $ 2F^2 + 4C^2 = 24 $- $ 4F + 16C = 24 $- None of the other choices are correctThis problem explores the concept of a Production Possibilities Frontier (PPF) where Robinson can allocate a limited number of hours to produce a combination of two goods.

Robinson is trapped on an island and can produce Fish (F) or coconuts (C) with his time. LF is labor…

Lc denote labor hours dedicated to fishing or gathering coconuts, respe inson's technological relationships for producing fish is given by: F = √LF inson's technological relationships for producing coconuts is given by: C = √Lc

Lc denote labor hours dedicated to fishing or gathering coconuts, respe inson's technological relationships for producing fish is given by: F = √LF inson's technological relationships for producing coconuts is given by: C = √Lc

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

**Problem Statement:**

Robinson is trapped on an island and can produce Fish (F) or Coconuts (C) with his time. Let $L_F$ and $L_C$ denote labor hours dedicated to fishing or gathering coconuts, respectively.

Robinson's technological relationships for producing fish is given by:

\[ F = \frac{1}{2} \sqrt{L_F} \]

Robinson's technological relationships for producing coconuts is given by:

\[ C = \frac{1}{4} \sqrt{L_C} \]

Which of the following correctly expresses the relationship between fish and coconuts along Robinson's PPF for a single 24 hour day (assume he doesn't sleep)?

**Options:**

- $ F^2 + 4C^2 = 6 $
- $ 2F^2 + 4C^2 = 24 $
- $ 4F + 16C = 24 $
- None of the other choices are correct

This problem explores the concept of a Production Possibilities Frontier (PPF) where Robinson can allocate a limited number of hours to produce a combination of two goods.

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