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An economy depends on two basic products, wheat and oil.  To produce 1 metric ton of...

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cbromm | (Level 1) Honors

Posted July 21, 2013 at 7:26 PM via web

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An economy depends on two basic products, wheat and oil.  To produce 1 metric ton of wheat requires .25 metric tons of wheat and .34 metric tons of oil.  Production of 1 metric ton of oil consumes .08 metric tons of wheat and .14 metric tons of oil.  Find the production that will satisfy a demand for 410 metric tons of wheat and 810 metric tons of oil.

Input-output matrix A = [ .25   .08 ]

                                    [ .34   .14 ]

How much wheat is required to satisfy the demand?

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted July 22, 2013 at 1:02 AM (Answer #1)

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We are given the technology matrix `A=([.25,.08],[.34,.14])` and external demand matrix (vector) `D=([410],[810])` and we are asked to find the production vector (matrix) X.

`X=(I-A)^(-1)D`

`=([.75,-.08],[-.34,.86])^(-1)([410],[810])`

`=([4300/3089,400/3089],[1700/3089,3750/3089])([410],[810])`

`=([2087000/3089],[3734500/3089])~~([675.62],[1208.97])`

So there is a need for approximately 676 metric tons of wheat.

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