An economy is based on three sectors agriculture manufacturi

An economy is based on three sectors, agriculture, manufacturing, and energy. Production of 1 unit of agriculture requires 0.4 units of agriculture, 0.2 units of manufacturing, and 0.3 units of energy. Production of 1 unit of manufacturing requires 0.3 units of agriculture, 0.2 units of manufacturing, and 0.5 units of energy. Production of 1 unit of energy requires 0.1 units of agriculture, 0.2 units of manufacturing, and 0.1 units of energy. Find the output for each sector that is needed to satisfy a final demand of 20 units of agriculture, 15 units of manufacturing, and 18 units of energy. Round answer to the nearest tenth of a unit.

Solution

let the output of agr-- be x

let the output of manuf --- be y

let the output of energy --- be z

Agri = 20 units

0.4x +0.3y +0.1z = 20 -----(1)

Manufacturing = 15 units

0.2x +0.2y +0.2z = 15 -----(2)

Energy = 18 units

0.3x +0.5y +0.1 z = 18 -----(3)

Solve the following equations:

we get Agriculture x= 36.25 = 36.3

Manufacturing y = 8.13 = 8.1

Energy z = 30.62 = 30.6