An applied maths problem to do with printing an amount of newspapers.
I have a requirement to pubish 350,000 copies of a newspaper.
2 presses with a capacity of 35,000 copies per hour can start at 22:00
This takes 5 hours to complete, but is too long.
So a second press with capacity of 20,000 copies per hour can start at 23:30
What is the quickest time, assuming no hold ups, that this can be done?
Really I need the formula to work this out, not the straight answer, so that if any variable changes I can just alter the variable (either print capacity or time that presses are available).
I know that optimum end time is 02:15
print capacity from 22:00 to 23:30 is 70,000
print capacity from 23:30 onwards is 90,000
105,000 copies are printed in first 1.5 hours
time of remaining run = remaining copies to print / print capacity
time of remaining run = (350,000 - 105,000) / 90,000
= 2.72 hours (approx 2 3/4 hours)
so end time is 23:30 + 2:45 = 02:15
so what can I use as a formula, please?