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D1 help

Gin is 45% alcohol by volume and tonic is non-alcoholic. Its required to mix gin and tonics which are at least 10% alcohol by volume and contain atleast 200ml of liquid but at most 30ml of alcohol

a) what are the greatest and least amounts of gin a drink can contain
b) what are the greatest and least amounts of tonic a drink can contain

I understand you would first make the constraints x?30, x+y?10, x+y?200 ,x?0, y?0,

Secondly do you need to draw a graph?

Any help would be appreciated :smile:
Original post by Nina8
Gin is 45% alcohol by volume and tonic is non-alcoholic. Its required to mix gin and tonics which are at least 10% alcohol by volume and contain atleast 200ml of liquid but at most 30ml of alcohol

a) what are the greatest and least amounts of gin a drink can contain
b) what are the greatest and least amounts of tonic a drink can contain

I understand you would first make the constraints x?30, x+y?10, x+y?200 ,x?0, y?0,

Secondly do you need to draw a graph?

Any help would be appreciated :smile:


A graph would be useful, but if you can do it without, fair enough.

I presume x is the amount of gin and y is the amount of tonic.

What constraints did you end up with? Several of those, as they, stands don't look right.

Since the gin is 45% alcohol by volume, then 100ml of gin gives 45 ml of alcohol.
(edited 10 years ago)
Reply 2
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Nina8
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8
Original post by ghostwalker
A graph would be useful, but if you can do it without, fair enough.

I presume x is the amount of gin and y is the amount of tonic.

What constraints did you end up with? Several of those, as they, stands don't look right.

Since the gin is 45% alcohol by volume, then 100ml of gin gives 45 ml of alcohol.



I had x>= 0 , y>=0 , 0.45x+y/x+y >= 0.10 (because it says atleast 10 percent alcohol), x+y >= 200 , and Im so confused how to put in atmost 30ml of alcohol.

Im just going in circles right now :confused:
Original post by Nina8

0.45x+y/x+y >= 0.10 (because it says atleast 10 percent alcohol)


That's not correct - the numerator. You need amount of alcohol over total amount >=0.1
There's no alcohol in tonic.


how to put in atmost 30ml of alcohol.


Amount of alcohol is 0.45x, hence 0.45x <= 30
Reply 4
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Nina8
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8
[QUOTE="ghostwalker;46479332"]That's not correct - the numerator. You need amount of alcohol over total amount >=0.1
There's no alcohol in tonic.



Amount of alcohol is 0.45x, hence 0.45x <= 30[/QUOTE

I meant (0)y which would make it a 0!! Thankyou so much you're a lifesaver :smile:) How would I work to get the greatest and least amount from there?

(sorry for being such a bother)
Original post by Nina8
...


Do a graph and plot the feasible region.
Reply 6
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Nina8
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Original post by ghostwalker
Do a graph and plot the feasible region.


And find the intersections right? THANKYOU SO MUCH, you're amazing :biggrin::biggrin:
Reply 7
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Welbeck
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so what should this have been: 0.45x+y/x+y >= 0.10?
Original post by Welbeck
so what should this have been: 0.45x+y/x+y >= 0.10?


There's no alcohol in the tonic, so:

0.45x/(x+y) >= 0.10

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