Matrix of production/2/Exercise

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

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

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.

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

What resources are necessary?

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

	${}R_{1}$	${}R_{2}$	${}R_{3}$
	${}12$	${}9$	${}13$

Which tuples of commodities can be produced from this without waste?

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