Constraints math problem?
You are the manager of a laundry. You need to get at least 78 cartloads of shirts processed and 114 cartloads of pants processed, you have two workers, pat can do 2 cartloads of shirts and 5 cartloads of pants in an hour chris can do 3 of each in an hour you pay them both $16/hour how many hours should you hire each worker so the work gets done with minimum labor costs (so that you know whether or not you got the right answer your total labor cost is $480)
your question is what are the constraints to a graph for this problem
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The variables for the problem are
C the number of hours that Chris works and
P the number of hours that Pat works
For shirts you have this constraint
2P + 3C >= 78
For pants you have
5P + 3C >= 114
The cost is
cost = 16P + 16C and you want to
minimize 16P + 16C (which works out to be the same as just minimizing P + C)
Let x represent the number of hours Pat works, and y symbolize the quantity of hours Chris works. Then our constraints are: 2x + 3y ≥ seventy eight [cartloads of shirts that must be processed] 5x + 3y ≥ 114 [cartloads of pants] and, of path, x ≥ zero and y ≥ zero The vertices of the viable discipline come out as (0,38), (12,18), and (39,0) with a purpose to result in the expected answer.