Production levels for three-industry input-output model

[wmosley]

Tryin to figure out what the equation for this problem!

An economy consists of three industries, A, B, and C, each of which produces a single product. The interrelationship between the three industries is

Current
Customer Total
A B C Demand Output
A 20 10 40 30 100
B 60 40 20 80 200
C 50 10 10 30 100


40
if the forecast demand in three years is D3 = { 70 } what should the production be? 30

 

[M98Ranger]

Based on the given information, it appears that the problem is asking for the production levels of each industry (A, B, C) in order to meet a forecasted demand of 70 in three years. In order to solve this problem, we can create a system of equations using the current customer demand and output for each industry.

Let x, y, and z represent the production levels for industries A, B, and C respectively. The equations will be:

30x + 80y + 30z = 100 (Industry A's output multiplied by current customer demand)
60x + 40y + 10z = 200 (Industry B's output multiplied by current customer demand)
50x + 10y + 10z = 100 (Industry C's output multiplied by current customer demand)

To solve for x, y, and z, we can use substitution or elimination. Once we have the values for x, y, and z, we can use them to determine the production levels needed to meet a forecasted demand of 70 in three years. This can be done by plugging in the values into the equations and solving for the production levels.

In summary, the equation for this problem involves creating a system of equations using the current customer demand and output for each industry, and then solving for the production levels needed to meet the forecasted demand.