Question

A large energy company produces electricity, natural gas, and oil. The production of a dollar's worth of

electricity requires inputs of $0.35 from electricity, $0.15 from natural gas, and $0.25 from oil. Production of a
dollar's worth of natural gas requires inputs of $0.35 from electricity, $0.15 from natural gas, and $0.20 from
oil. Production of a dollar's worth of oil requires inputs of $0.10 from each sector. Find the output for each
sector that is needed to satisfy a final demand of $25 billion for electricity, $15 billion for natural gas, and $20
billion for oil.

Answer 1

E = 64.05

NG = 52.29

O = 35.15

Explanation:

With the statement we can create a system of 3X3 equations that would be as follows:

E = electricity

NG = natural gas

O = oil

0.35 * E + 0.15 * NG + 0.25 * O = 25

0.35 * E + 0.15 * NG + 0.2 * O = 15

0.1 * E + 0.1 * NG + 0.1 * O = 20

If we pass this system equations to matrix and subtract it from the identity matrix we would have the following:

0.65 * E - 0.15 * NG - 0.25 * O = 25

-0.35 * E + 0.85 * NG - 0.2 * O = 15

-0.1 * E - 0.1 * NG + 0.9 * O = 20

Solving this system of equations around here can be very long and impractical, therefore, I attach a photo of the process:

And the answer is:

E = 64.05

NG = 52.29

O = 35.15