A printer has a contract to print 100,000 posters for a political candidate. He can run the posters by using any number of plates from 1 to 30 on his press. If he uses x metal plates, they will produce x copies of the poster with each impression of the press. The metal plates cost $30.00 to prepare, and it costs $202.80 per hour to run the press. If the press can make 1000 impressions per hour, how many metal plates should the printer make to minimize costs?
+130511 I'm not totally confident about this answer, but I'll give it a shot.....!!!!
The number of posters he can print per hour equals the number of impressions he can make per hour x the number of plates used in each impression = 1000x
And the number of hours it will take him is given by 100,000/(1000x) = 100/x
And the cost per hour equals 202.80
I'm assuming that each plate costs $30 to prepare....so the total cost of the plates is just $30x
So the total cost is given by:
C =[100/x)]202.80 + 30x simplify
C = 20280/x + 30x
So.....take the derivative and set it to 0
C' = -20280/x2 + 30
Set to 0
-20280/x2 + 30 = 0 simplify
20280 = 30x2
x2 = 2028/3
x2 = 676
x = 26 .....so 26 plates should be used
+130511 I'm not totally confident about this answer, but I'll give it a shot.....!!!!
The number of posters he can print per hour equals the number of impressions he can make per hour x the number of plates used in each impression = 1000x
And the number of hours it will take him is given by 100,000/(1000x) = 100/x
And the cost per hour equals 202.80
I'm assuming that each plate costs $30 to prepare....so the total cost of the plates is just $30x
So the total cost is given by:
C =[100/x)]202.80 + 30x simplify
C = 20280/x + 30x
So.....take the derivative and set it to 0
C' = -20280/x2 + 30
Set to 0
-20280/x2 + 30 = 0 simplify
20280 = 30x2
x2 = 2028/3
x2 = 676
x = 26 .....so 26 plates should be used
