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Question of the Day: Finite Mathematics

It is suggested (but not necessary) that you use a calculator with matrix capability to work this problem.

A village is famous for being the most prolific producer in the world of ambrosia, butterbeer, and silphium. Every year, they try to meet the world's demand for 20,000 kg of ambrosia, 30,000 kg of butterbeer, and 15,000 kg of silphium. However, the production of these items requires the consumption of these items as well:

The production of 1 kg of ambrosia requires the use of 0.05 kg of butterbeer and 0.08 kg of silphium;

The production of 1 kg of butterbeer requires the use of 0.04 kg of ambrosia and 0.09 kg of silphium; and,

The production of 1 kg of silphium requires the use of 0.06 kg of ambrosia and 0.07 kg of butterbeer.

Use a Leontief model to determine how much silphium (nearest hundred kilograms) must be produced to meet the demand.

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