How many presses should be used?

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Question from Sarah, a student:

Hi! I am in Calculus and this problem is on my study guide and i just can't figure it out!?

A printing company had eight presses, each of which can print 300 copies per hour. It costs $5.00 to set up each press for a run and 12.5+6n dollars to run n presses for an hour. How many presses should be used to print 6000 copies most profitably? Let h equal the number of hours used to print the 6000 copies.

Hi Sarah,

Each press can print at the same rate, 300 copies per hour so the job will take h = 6000/300 = 20 hours of printing time spread across the n presses being used. Thus the presses will run for 20/n hours each. If the number of presses used is n then the cost of the job is

C(n) = $5.00 × n + (12.5 + 6n) × 20/n

I hope this helps,
Harley

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