# An economy depends on two basic products, wheat and oil. To produce 1 metric ton of wheat requires 0.23 metric tons of wheat and 0.33 metric tons of oil. Production of 1 metric ton of oil consumes...

An economy depends on two basic products, wheat and oil. To produce 1 metric ton of wheat requires 0.23 metric tons of wheat and 0.33 metric tons of oil. Production of 1 metric ton of oil consumes 0.09 metric tons of wheat and 0.1 metric tons of oil. Find the production that will satisy a demand for 440 metric tons of wheat and 880 metric tons of oil.

Input-outpu matrix A=[0.23 0.09]

[0.33 0.1]

How many metric tons of wheat are required to satisfy the demand?

How many metric tons of oil are required to satisfy the demand?

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We have the input-output matrix

[0.23 0.09] = A

[0.33 0.1]

We subtract the identity matrix from this:

[I] - A = [1 0] - [0.23 0.09] = [0.77 -.09] = C

[0 1] [0.33 0.1] [-0.33 0.9]

We find the inverse of this. We can use a graphing calculator for this:

`C^(-1)` = [1.357 0.136]

[ 0.498 1.162]

The demand matrix is D:

D = [ 440 ]

[ 880 ]

We multiply these together to find the production matrix:

`` * D= [1.357 0.136] * [ 440 ] = [ 716.42 ]

[0.498 1.162] [ 880 ] [ 1240.46 ]

So, we could produce 716.42 metric tons of wheat and 1240.46 metric tons of oil give 440 metric tons of wheat and 880 metric tons of oil.