Jewerly

A company produces the three

alloys "gold leaf" $($BG$),$ "light

gold" $($HG$),$ and "dark gold" $($DG$)$

from the metals gold $(Au),$ silver

$(Ag)$ and copper $(Cu).$ In a second

production stage, these alloys are

processed into bracelets $($Reif$)$ and

necklaces $($Kette$).$ The figure shows

the material consumption for each production stage. The numbers are units of

measure.

a$)$ Show the material consumption for each production stage in the form of a labeled

matrix and calculate how many units of the three metals are required to produce a

bracelet and a necklace.

b$)$ The two customers "Gold Mayer" and "Gold Brillant" place the following order:

"Gold Mayer" $80$ bangles, $70$ chains, "Gold Brillant": $110$ bracelets, $240$ necklaces.

Calculate how many units of the three metals $(Au,Ag,Cu)$ are required for each order.

c$)$ Calculate how many units of gold leaf, light gold and dark gold can be made from $760$ units of

gold, $195$ units of silver and $290$ units of copper. Control solution: $(20$;$35$;$50).$