In Gotham City, the departments of Administration (A), Health (H), and Transport

Question

In Gotham City, the departments of Administration (A), Health (H), and Transportation (T) are interdependent. For every dollar's worth of services they produce, each department uses a certain amount of the services produced by the other departments and itself, as shown in the table below. Suppose that, during the year, other city departments require $0.20 million in Administrative services, $1.25 million in Health services, and $1.09 million in Transportation services. What does the annual dollar value of the services produced by each department need to be in order to meet the demands? (Round your answers to two decimal places.)

<th colspan="5" '=""> Department    A    H    T    A $0.20 0.10 0.20 Buy H 0.10 0.10 0.20 T 0.20 0.40 0.30

Explanation / Answer

Let Annual value of services produced by A, H and T be X, Y and Z respectively.

1.

From table:
In $1 produced by A, H and T consume $0.1 and $0.2 respectively.
Derived:
In X produced by A - H and T consume 0.3X together.
Given:
Other departments (H and T) require $0.2Million of A services.
Conclusion:
0.3X = $0.2 Million

.:X = $ 0.67Million
.: Annual value of services produced by Administrative department = $ 0.67Million

2.

From table:
In $1 produced by H, A and T consume $0.1 and $0.2 respectively.
Derived:
In Y produced by H - A and T consume 0.3Y together.
Given:
Other departments (A and T) require $1.25Million of H services.
Conclusion:
0.3Y = $1.25 Million

.:Y = $ 4.17Million
.: Annual value of services produced by Health department = $ 4.17Million

3.

From table:
In $1 produced by T, A and H consume $0.2 and $0.4 respectively.
Derived:
In Z produced by T - A and H consume 0.6X together.
Given:
Other departments (A and H) require $1.09Million of T services.
Conclusion:
0.6Z = $1.09 Million

.:Z = $ 1.82Million
.: Annual value of services produced by Transport department = $ 1.82Million

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