An wine-producing industry produces wine and vinegar. Twice the production of wine is always smaller than or equal to than the vinegar production plus four units. Determine the region of validity of the inequation (and to draw it).

a) Identify the variables.

b) Express the restriction as an inequation of the variables.

c) Give the expression of the straight line associated with the restriction (and draw it).

### Development:

a) $$x=$$ production of wine. $$\ y=$$ production of vinegar.

b) $$2\cdot x \leqslant y+4 \Rightarrow 2\cdot x-y \leqslant 4$$

c) $$2\cdot x=y+4 \Rightarrow y=2x-4$$

Trying point $$(x=0,y=0)$$ it is seen that the inequation is satisfied: $$2\cdot 0-0 \leqslant 4$$. Therefore the validity region is the semiplane over the straight line.

### Solution:

The validity region is the semiplane over the straight line.