Cost of Production

[vishwas.arora]

The cost of production of a certain instrument increases with the number of units produced. What is the cost of production for 270 units?

(1) The cost of production for 300 units is $300.
(2) The cost of production is directly proportional to the number of units produced.

Expert replies please.
OA after some discussion.

Thanks

[kmittal82]

(1) Doesn't give us the exact relationship between cost and number of units. The relationship could be linear, square, or any other function. Not sufficient

(2) States the same info as given in the question, just in slightly more mathematical terms

I think its (E). OA ?

[GmatKiss]

IMO:C

1: not sufficient
2: not sufficient

from 2 we know cost is directly proportional to no of units.
Along with 1, it shows us the cost is 1-1, 2-2, 3-3 ... 300-300, which is directly proportional.

therefore cost of 270 units is 270!

OA please!

[kmittal82]

Along with 1, it shows us the cost is 1-1, 2-2, 3-3 ... 300-300, which is directly proportional.

But this doesn't support the original question which says that "The cost of production of a certain instrument increases with the number of units produced" ? If 1-1, 2-2 etc is true, then the cost of production is not increasing with number of units, its staying the same per unit.

[GmatKiss]

oops! yup, true
thanks for pointing out!

IMO:E

[vishwas.arora]

The question stem just tells us that the cost of producing, say n components, increases with n.

But Cost, C can be a linear or quadratic or any increasing function of n

Statement 1 does not provide info about the function, except that cost of producing 300 units is $300.

Statement 2 alone just says that C is directly proportional to n, i.e. C = C' + kn
where C' is the cost of producing zero components, or the fixed cost.

I think we cannot assume C' to be 0, unless provided any info about the boundary condition

When we combine both the equations,
we still cannot precisely find both k and C'
I am again assuming that fixed cost is not zero.

Thus IMO E.

But somehow in the OA they have assumed, in fact not even discussed about, the fixed cost component.
OA is C

Can we please have some expert comments.

Thanks all !

[gmatboost]

2 comments:

1. Directly proportional means that C = kn. There is no "fixed cost component" in direct proportions.
If St2 said something like...
"The cost of producing each additional unit is constant"
...then we would need to consider the initial fixed cost.
So, I agree with those that said the answer was C.

2. There is some ambiguity in the question. On the GMAT, this would never be the case.

The cost of production of a certain instrument increases

Does that mean total cost, or marginal cost?
kmittal82 is assuming they mean marginal cost.
GMATKiss assumed they meant total cost.

I think either interpretation could be correct given the current wording. But don't worry, the test will make it clear to you.

[GmatKiss]

Thanks for the clarifications Boost