The total population of a tropical island is 200 people. Every day each person either goes fishing or gathers fruit. All food is shared between the islanders and none is traded outside the island. The production of 5 units of fish requires four people and one unit of fish. The production of 1 unit of fruit requires one person. Each person in the island requires 2/5 units of fish and 3/5 units of fruit. (a) Write the input-output matrix A for the closed Leontief economic model which describes this island. Hint: the sectors are fish, fruit and people (labour). (b) Solve the closed Leontief economic model using Gauss-Jordan elimination by hand, showing working, to find the production vector. (c) On this island, how many people go fishing and how many people gather fruit?
The total population of a tropical island is 200 people. Every day each person either goes fishing or gathers fruit. All food is shared between the islanders and none is traded outside the island. The production of 5 units of fish requires four people and one unit of fish. The production of 1 unit of fruit requires one person. Each person in the island requires 2/5 units of fish and 3/5 units of fruit. (a) Write the input-output matrix A for the closed Leontief economic model which describes this island. Hint: the sectors are fish, fruit and people (labour). (b) Solve the closed Leontief economic model using Gauss-Jordan elimination by hand, showing working, to find the production vector. (c) On this island, how many people go fishing and how many people gather fruit?
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
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Transcribed Image Text:The total population of a tropical island is 200 people. Every day each
person either goes fishing or gathers fruit. All food is shared between
the islanders and none is traded outside the island. The production of
5 units of fish requires four people and one unit of fish. The production
of 1 unit of fruit requires one person. Each person in the island requires
2/5 units of fish and 3/5 units of fruit.
(a) Write the input-output matrix A for the closed Leontief economic
model which describes this island. Hint: the sectors are fish, fruit
and people (labour).
(b) Solve the closed Leontief economic model using Gauss-Jordan
elimination by hand, showing working, to find the production
vector.
(c) On this island, how many people go fishing and how many people
gather fruit?
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