Posted by Andrew on Friday, December 7, 2012 at 6:15am.
number of craftmen --- x
number of apprentices --y
500x + 100y ≥ 2000 ---> 5x + y ≥ 20 for ceramic
100x + 200y ≥ 1600 ---> x + 2y ≥ 16 for vinyl
cost = 200x + 120y
sketch the first two relations in x and y
we need the closest integer-point to their intersection point of (2.67 , 6.67)
which would be (3,7)
So 3 craftsmen and 7 apprentices would do the job and be cheapest.
check:
with (3,8) --> 1500+800 or 2300 ceramic, job done
---------> 300+1600 or 1900 vinyl, job done
cost = 200(3) + 120(8) = $1560
with (3,7) --> 1500+700= 2200 ceramics, job done
----------> 300+ 1400= 1700 vinyl, job done
cost = 200(3) + 120(7) = $1440
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