Matrix of production/2/Exercise

Out of the resources ${\displaystyle {}R_{1},R_{2}}$ and ${\displaystyle {}R_{3}}$, several commodities ${\displaystyle {}P_{1},P_{2},P_{3},P_{4}}$ are produced. The following table shows, how much of the resources is needed to produce the commodities (always in suitable units).

${\displaystyle {}R_{1}}$ ${\displaystyle {}R_{2}}$ ${\displaystyle {}R_{3}}$
${\displaystyle {}P_{1}}$ ${\displaystyle {}6}$ ${\displaystyle {}2}$ ${\displaystyle {}3}$
${\displaystyle {}P_{2}}$ ${\displaystyle {}4}$ ${\displaystyle {}1}$ ${\displaystyle {}2}$
${\displaystyle {}P_{3}}$ ${\displaystyle {}0}$ ${\displaystyle {}5}$ ${\displaystyle {}2}$
${\displaystyle {}P_{4}}$ ${\displaystyle {}2}$ ${\displaystyle {}1}$ ${\displaystyle {}5}$

a) Establish a matrix, which computes, applied to a four-tuple of commodities, the required resources.

b) The following table shows how much of each commodity shall be produced in a month.

 ${\displaystyle {}P_{1}}$ ${\displaystyle {}P_{2}}$ ${\displaystyle {}P_{3}}$ ${\displaystyle {}P_{4}}$ ${\displaystyle {}6}$ ${\displaystyle {}4}$ ${\displaystyle {}7}$ ${\displaystyle {}5}$

What resources are necessary?

c) The following table shows how much of each resource is delivered on a certain day.

 ${\displaystyle {}R_{1}}$ ${\displaystyle {}R_{2}}$ ${\displaystyle {}R_{3}}$ ${\displaystyle {}12}$ ${\displaystyle {}9}$ ${\displaystyle {}13}$
Which tuples of commodities can be produced from this without waste?