# 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?

steveschoen | Certified Educator

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.