An economy consists of three industries: coal, steel and transport.[10] Each unit produced by one of the industries (a unit will be taken as £l’s worth of value of production) requires inputs from
possibly its own industry as well as other industries. The required inputs as well as the manpower requirements (also measured
in £) are given in Table 10.1. There is a time lag in the economy so that output in year 
requires an input in year 
.
Output from an industry may also be used to build productive capacity for itself or other industries in future years. The
inputs required to give unit increases (capacity for £l’s worth of extra production) in productive capacity are given in Table 10.2. Input from an industry in year results in a (permanent) increase in productive capacity in year 
.
Table 10.1:
|
Outputs (year |
|||
|---|---|---|---|
|
Inputs (year |
Coal |
Steel |
Transport |
|
Coal |
0.1 |
0.5 |
0.4 |
|
Steel |
0.1 |
0.1 |
0.2 |
|
Transport |
0.2 |
0.1 |
0.2 |
|
Manpower |
0.6 |
0.3 |
0.2 |
Table 10.2:
|
Outputs (year |
|||
|---|---|---|---|
|
Inputs (year |
Coal |
Steel |
Transport |
|
Coal |
0.0 |
0.7 |
0.9 |
|
Steel |
0.1 |
0.1 |
0.2 |
|
Transport |
0.2 |
0.1 |
0.2 |
|
Manpower |
0.4 |
0.2 |
0.1 |
Stocks of goods may be held from year to year. At present (year 0) the stocks and productive capacities (per year) are given in Table 10.3 (in £m). There is a limited yearly manpower capacity of £470m.
It is wished to investigate different possible growth patterns for the economy over the next five years. In particular it is desirable to know the growth patterns which would result from pursuing the following objectives:
-
Maximizing total productive capacity at the end of the five years while meeting an exogenous consumption requirement of £60m of coal, £60m of steel, and £30m of transport in every year (apart from year 0).
-
Maximizing total production (rather than productive capacity) in the fourth and fifth years, but ignoring exogenous demand in each year.
-
Maximizing the total manpower requirement (ignoring the manpower capacity limitation) over the period while meeting the yearly exogenous demands of (i).