# Thread: How long for a run of papers

1. ## How long for a run of papers

Hi
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?

Thank you

2. ## Re: How long for a run of papers

Ok done it.

press capacity 1 = x = 30,000 copies per hour
press capacity 2 = y = 35,000 copies per hour
press capacity 3 = z = 20,000 copies per hour

presses x and y start at 22.00
press z starts at 23.30

planned quantity = Q = 350,000

OK
2 presses work for t hours
1 press works (t-1.5) hours

(capacity 1) t + (capacity 2) t + (capacity 3) (t-1.5) = 350,000

xt + yt + z(t-1.5) = Q
xt + yt + zt - z(1.5) = Q
xt + yt + zt = Q + z(1.5)

t = (Q + z(1.5)) / xt + yt + z

In real terms with real numbers then
The two presses work for t hours. The third one for ( t - 1.5 ) hrs

70000 t + 20000 ( t - 1.5 ) = 350000

70000 t + 20000 t - 30000 = 350000

90000 t = 380000

......... t = 380000/ 90000

......... t = 4.2 = 4hrs 13 min

The machines started at 22 hrs, plus 4 hrs 13 min . It ends at 2 hrs 13 min

It ends at 2 hrs 13 min

Ta dah!
Not all my own work, sorry.

3. ## Re: How long for a run of papers

Originally Posted by froodles01
Hi
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
You mean a third press don't you?
Suppose the run goes T hours after 22:00. Then the first two presses will each have done a total of 35000T copies and the two together will have done 2(35000T)= 70000T copies.
Since the third press started 1 and half hours later, it will have run for x- 1.5 hours and will have completed 20000(x- 1.5)= 20000x- 30000 copies.
The three presses, together will have done 70000T+ 20000T- 30000= 90000T- 30000 copies and we want that to be equal to 350000 copies:
Solve the equation 90000T- 30000= 350000.

90000T= 380000 so T= 380000/90000= 4.22222= 4 and 2/9 hours.
(I get 4 hours, 13 minutes, and 20 seconds so the run would be finished at 2:13:20 AM.)

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).
Unfortunately, mathematics does not often consist of just plugging numbers into formulas. Hopefully you can understand my and ***'s reasoning to see how the calculations would be modified in other circumstances.

I know that optimum end time is 02:15
Then, unfortunately, you know wrong.

print capacity from 22:00 to 23:30 is 70,000
70000 copies per hour, don't forget that part.

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)
Were you told to round to the nearest quarter hour? You didn't tell us any ofthat.

so end time is 23:30 + 2:45 = 02:15

so what can I use as a formula, please?

Thank you
The only 'formula' involved is precisely the one you used to find all of those numbers.