Working on this for a couple of hours, any help?
Input -output matrix
F S C
F .1 0 .2
S .2 .1 .4
C 0 0 .1
F= Food
S=Shelter
C=Clothing
1)What should the total production of the three industries be to generate a $900,000 surplus each?
I gotthe following for 1) F=1,224,000 S=1,719,000 and C=999,000. Not sure though
2) In another year, no shelter related products can leave the community, but the community continues to meet the goal of $900,000 of food and clothing. What should the total production be?
To find the total production that generates a $900,000 surplus for each industry, we need to follow these steps:
1) Start with the input-output matrix:
```
F S C
F .1 0 .2
S .2 .1 .4
C 0 0 .1
```
2) Let's assume the total production for each industry is represented by the variables F, S, and C respectively. We want to find the values of F, S, and C that result in a surplus of $900,000 for each industry.
3) We can set up the following equations based on the given information:
Total value produced by Food industry (F) = 0.1F + 0S + 0.2C
Total value produced by Shelter industry (S) = 0F + 0.1S + 0C
Total value produced by Clothing industry (C) = 0.2F + 0.4S + 0.1C
4) The surplus generated by each industry is their total value produced minus the amount needed to meet the goal of $900,000. For example, for the Food industry, the surplus is (0.1F + 0S + 0.2C) - $900,000 = 0.1F + 0.2C - $900,000. Similarly for the other industries.
5) Since we want a $900,000 surplus for each industry, we can set up the following equations:
0.1F + 0.2C - $900,000 = 0
0F + 0.1S + 0C - $900,000 = 0
0.2F + 0.4S + 0.1C - $900,000 = 0
6) Now we can solve these equations to find the values of F, S, and C that satisfy these conditions.
For your first question, you calculated F = 1,224,000, S = 1,719,000, and C = 999,000. Without more information, it is difficult to determine if these values are correct. However, you can check if they satisfy the equation system by substituting them into the equations and verifying if they result in a $900,000 surplus for each industry.
For your second question, since no shelter-related products can leave the community, we need to set the value of S to 0 in the equations:
0.1F + 0.2C - $900,000 = 0
0F + 0.1(0) + 0C - $900,000 = 0
0.2F + 0.4(0) + 0.1C - $900,000 = 0
Now, solve these equations to find the values of F and C that satisfy the conditions.