$4.(12$ points$)$ Consider a Leontief economy consisting of two sectors: wine

and cheese. Workers can either be assigned as cheesemakers, to produce

one pound of cheese each, or winemakers, to produce one litre of wine

each. Every worker must be fed half a pound of cheese and half litre of

wine to stay productive.

a$)(6$ points$)$ Suppose the economy aims to export $50$ pounds of cheese

and $100$ litres of wine. Let

c

be the number of cheesemakers and

w

the number of winemakers. Summarise this economy in matrix form.

b$)(3$ points$)$ Does this economy have a unique solution? Justify your

answer

without

solving the system.

c$)(3$ points$)$ Now suppose each worker must be provided a third of a

pound of cheese $($instead of a half$).$ How many cheesemakers and

winemakers are needed in this economy?