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Extreme value problem:

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by \'manpreet singh » Sun Jul 01, 2012 9:27 pm
Q.1)The guests at a football banquet consumed a total of 401 pounds of food.If no individual guest consumed more than 2.5 pounds of food, what is the minimum number of guests that could have attended the banquet?

I solved as below....

401/2.5 =160.4

Here I am stuck up, should I round up or round down??160 or 161
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by Anurag@Gurome » Sun Jul 01, 2012 11:32 pm
'manpreet singh wrote:Q.1)The guests at a football banquet consumed a total of 401 pounds of food.If no individual guest consumed more than 2.5 pounds of food, what is the minimum number of guests that could have attended the banquet?
Algebraic Approach:
It is always better to form an inequality for this type of problems. Then you won't be stuck with such confusion.

Say, number of guests is N and each guest has P pounds of food.
Hence. NP = 401 and P ≤ 2.5

So, N = 401/P ≥ 401/2.5
--> N ≥ 160.4

Hence, minimum value of N is 161.
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by Anurag@Gurome » Sun Jul 01, 2012 11:42 pm
Conceptual Approach:
To minimize the number of guests we need to maximize the amount of food each of them have consumed as their product is constant.

Hence, minimum number of guests = (401/2.5) = 160.4
As 160.4 cannot be the number of guests, minimum number of guests is the next integer, i.e. 161.
Here I am stuck up, should I round up or round down??160 or 161
If the minimum number of guests is 160, then 160*2.5 = 400.
Therefore, some of the guests must have consumed more than 2.5 pounds of food to get maintain the total of 401 pounds. That is not possible.
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by \'manpreet singh » Mon Jul 02, 2012 9:21 am
Anurag@Gurome wrote:Conceptual Approach:
To minimize the number of guests we need to maximize the amount of food each of them have consumed as their product is constant.

Hence, minimum number of guests = (401/2.5) = 160.4
As 160.4 cannot be the number of guests, minimum number of guests is the next integer, i.e. 161.
Here I am stuck up, should I round up or round down??160 or 161
If the minimum number of guests is 160, then 160*2.5 = 400.
Therefore, some of the guests must have consumed more than 2.5 pounds of food to get maintain the total of 401 pounds. That is not possible.

Thanks Anurag you are a genious!!! confusion sorted!! :D
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