An economy consists of coal electric and steel sectors For e

An economy consists of coal, electric, and steel sectors. For each $1.00 of output, the coal sector needs $0.04 worth of coal, $0.03 worth of electric, and $0.01 worth of steel; the electric sector needs $0.06 worth of coal, $0.05 worth of electric, and $0.08 worth of steel; and the steel sector needs $0.23 worth of coal and $0.09 worth of steel. Suppose that $7 billion of coal, $4 billion of electricity, and $5 billion of steel are produced. How much of each industry\'s output will be available for consumption?

There will be $___ billion of coal, $___ billion of electricity, and $___ billion of steel available for consumption.

Solution

Let available outputy from coal industry be $ x billion

from electricity industry be $y billion

from steel be $z billion

So, 0.04x + 0.03y + 0.01z = 7

0.06x + 0.05y + 0.08z = 4

0.23x +0.09z = 5

Solution for above comes out to be x = 6040/91 billion( coal) ; y = 1280/7 billion( electricty) ; z = - 10380/ 91 billion( steel)

The last value comes out to be -ve which is not consistent.The data given in the question needs to be rechecked from source.

However method remains same

Solve the above equations to get x, y , z: