Another one

[mishum2000]

A manufacturer can save x dollars per unit in production costs by overproducing in certain seasons. If storage costs for the excess are y dollars per unit per day (x>y), which of the following expresses the maximum number of days that n excess units can be stored before the storage costs exceed the savings on the excess units ?

A x-y
B (x-y)n
C x/y
D xn/y
E x/yn

[wydiwyg]

Ans E> x/yn

[mishum2000]

Please detail your reasoning.

[wydiwyg]

A manufacturer can save x dollars per unit.

So $x is the cost of 1 unit.
For 1 day the storage cost for 1 unit is $y.
i.e $y is the storage cost for 1 unit for 1 day.
$ny is the storage cost of n units for 1 day.
$1 is the storage cost of n units for 1/ny day.
$x is the cost of of excess n units for x/ny days.

Am i right. Please correct me if i am worng.

[seemahesh]

i think ans is C:x/y
what is actual ans ???

solution:
for n units he got $nx money.
but to store it, he has to give $y per unit per day ;so for n units he has to pay $ny per day . now for $nx he needs nx/ny days
so ans is x/y.

seema

[mishum2000]

C is the right one....indeed seemahesh

[nowisthetime]

I agree with seemahesh. A very simple reasoning would be the following. Supposing the guy saves $10 a day per unit, and the storage cost is $2 per day (for each unit), then he can only store it for 5 days before the cost exceeds the benefit. Thus x/y = 10/2 = 5 days. Since this happens for each unit, n is irrelevant.

Note: If one can see that n doesn´t matter early on, the problem is reduced to choosing between alternatives a) and c), which of course is much faster.

D

[socialelite]

should be ny/x, I think
A manufacturer can save x dollars per unit in production costs by overproducing in certain seasons. If storage costs for the excess are y dollars per unit per day (x>y), which of the following expresses the maximum number of days that n excess units can be stored before the storage costs exceed the savings on the excess units
Assume N is the max of that day, N*x>=ny, so N=ny/x

[economicus]

I think it's C (x/y). Socialelite, I think that your answer forget that y represents the cost per unit.

assume, that we save $10 per unit. And the cost is $5 PER UNIT. So if we have 3 products:

10x3 (total cut) = 3x5xd
d= [10x3/]/ [3x5] = 10/5 = x/y (2 days)

if we use nx/y we get 3x10/5=6 ...but this mean that

3x10=5x6.....but 5 is the cost per unit and not the cost of all units together.

[kronique]

C) x/y