Projects - Cengage Learning

Appendix C C-93
n x units of that resource. Now we use this proportionality assumption, the
first row of figures in Table 1, and the definitions of x, y, and z, to write
(internal demands for steel) 0.04x 0.02y 0.16z
Using this last equation to substitute in equation (1), we obtain
0.04x 0.02y 0.16z 308 x
0.96x 0.02y 0.16z 308
(2)
Equation (2) is our first of three equations in three unknowns. A second equation
can be generated in the same manner, but using coal, rather than steel,
as the output under consideration. Again, similarly, a third equation can be
obtained by starting with electricity rather than steel.
Working in groups or individually, obtain the remaining two equations and
then solve the resulting system. As a check, the required answers are x 500 units
of steel, y 600 units of coal, and z 1000 units of electricity. Suggestion:
Work on this in groups. Then after your group has obtained the correct answers
and you are clear on the details, work individually on the next problem.
PART II: A Problem to Do and Then to Write Up on Your Own
Consider a three-sector economy: plastics, energy, and transportation. The production
of 1 unit of plastics requires 0.02 of unit plastics, 0.04 unit of energy, and
0.05 unit of transportation. The production of 1 unit of energy requires 0.03 unit
of plastics, 0.08 unit of energy, and 0.01 unit of transportation. The production
of 1 unit of transportation requires 0.01 unit of plastics, 0.02 unit of energy, and
0.06 unit of transportation. The external demands for plastics, energy, and transportation
are 22.76 units, 36.68 units, and 43.45 units, respectively.
(a) Display the given data using tables similar to Tables 1 and 2.
(b) How many units should each sector produce in order to satisfy both the
internal and external demands on the economy? Hint for checking: The
final answers turn out to be integers.