A bottling plant has 151,550 bottles with a capacity of 355 mL, 123,000 caps, and 33,500 L of beverage....?

(a) How many bottles can be filled and capped?
(b) How much of each item is left over?
#"____"# L of beverage?
#"____"# bottles?
#"____"# caps?
(c) Which component limits the production?

  • number of bottles
  • number of caps
  • volume of beverage

1 Answer
anor277
Jan 26, 2018

Well, for a start, you have not got enuff caps for the given number of bottles.....but perhaps you will not need all the caps....

Explanation:

And let us address the bottle capacity....and this is given by the product...we know that #1*mL-=10^-3*L#

#151,500*"bottles"xx0.355*L*"bottle"^-1-=53782*L#...and so at least you got the bottle capacity.

The number of bottles you need is given by the quotient...

#(33500*L)/(0.355*L*"bottle"^-1)=94366*"bottles"#...and you got enuff caps.... The limiting quantity is the beverage...and you got reserve bottles and caps for the breakages and the failed seals that will undoubtedly occur.

If you ever brew beer or ginger beer or home (and this is something that it is easy to do, and you get VERY good results). most of the time the limiting quantity is the bottles....the which you have to collect, and carefully clean and sanitize.

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