Question

determine the total output required from each industry in order to meet both consumer and between industry demand.

economy has three industries A B and C these industries have annual consumer sales of 30, 50, and 60(in billions of dollars) respectively. for every dollar of goods A sells, A requires 10 cents of good from B and 15 cents of goods from C. for every dollar B sells , B requires 15 cents from of goods from A and 20 cents of goods from C. for each dollar of goods C sells, C requires 20 cents of goods from A and 10 cents of good from B

Answer 1

We will write 3 linear equations from the given data and then solve it using determinants.

Let 'a, b,c' be the output quantities of A,B and C respectively.

This is because 30 pieces of a is sold to final consumer, 0.15 piece of a is needed for every b and 0.2 pieces of a is needed for every c.

Similarly,

Rearranging the equation to standard form,

Now, we will solve it using determinants.

Where,

Similarity,

That is, output from A,B and C are 55.77, 63.69 and 81.10 respectively.