A certain clothing manufacturer makes only two types of men's blazer:

Question

A certain clothing manufacturer makes only two types of men's blazer: cashmere and mohair. Each cashmere blazer requires 4 hours of cutting and 6 hours of sewing. Each mohair blazer requires 4 hours of cutting and 2 hours of sewing. The profit on each cashmere blazer is $40 and the profit on each mohair blazer is $35. How many of each type of blazer should the manufacturer produce each week in order to maximize its potential weekly profit on blazers?

(1) The company can afford a maximum of 200 hours of cutting per week and 200 hours of sewing per week.
(2) The wholesale price of cashmere cloth is twice that of mohair cloth.

LighthousePrep · Answer

I think this question is tricky because it is tempting to start doing the calculations. Because it is a data sufficiency question, really all you need to know is whether you have enough information to find the answer. No need to actually calculate how many of each the manufacturer should produce.

So here's how I set up the problem:

I know profit per product, I know effort per product by activity. All I need to know is capacity of each activity.

Statement 1: Gives me capacity for each activity. Therefore I should be able to figure out how to maximize profitability.

Eliminate B, C and E.

Statement 2: Relative wholesale pricing is irrelevant since we are already given the profit per product in the premise of the problem. This statement is insufficient.

Eliminate D.

Correct answer: A

DangerPenguin · Answer

I agree I also got A. Took me around 1min30sec.

Profit
cashmere 4hr/cutting 6hr/sewing $40
mohair 4hr/cutting 2hr/sewing $35
We need to find out how many of each type of blazer they should sell in order to maximize profits. In order to find this answer, we need to find out how many hours they work on each of these tasks.

Statement 1: sufficient
Knowing the maximum # of hours they can devote and already given the info on how many hours each task takes for the 2 types of blazers, we can use this statement to figure out how to maximize profit which is what we are being asked. No need to calculate since this is data sufficiency. Eliminate answer choices B, C, and E.

Statement 2: not sufficient
Doesn't give us any relevant info.

Answer A!

stne · Answer

Dear Moderator , 
Please provide OA and OE .
I also chose A .
The time for each Blazer is limited by its slowest process.
So for Cashmere , 6 hours of sewing will decide how many of these can be made.
For Mohair 4 hours of cutting will decide how many of these can be made.
So in 200 hours of cutting and sewing , max 33 cashmere or 50 Mohair can be made.
Cashmere profit = 33*40=1320 , Mohair profit = 50*35=1750 , hence it is more profitable to make Mohair Blazers.
( However I am not sure if both the blazers can be combined for even greater profit )

Statement B- since we are already given the profit , we do not need the purchase price .

kornn · Answer

Dear  IanStewart ,

How do we possibly know that producing 25 cashmere and mohair blazers each yields the maximum profits?

Do we have to do trail and error by gradually decreasing/increasing the number of cashmere blazers and see the corresponding number of mohair blazers, then sum up together?

Is there any other time-efficient approach?

IanStewart · Answer

The whole question doesn't make logical sense. In general, it makes no sense to ask a maximization problem as a DS question, because the answer to the question changes depending on what restrictions you have. Here, reading only the stem, it's possible there is a limit on the number of cutting hours we have, or on sewing hours, or possibly also on total hours of work, or on capital the person can invest in raw materials, or on the total amount of raw materials available, among other things. Each new restriction you add potentially changes the answer to a maximization problem, so there's no way to know what kind of information is sufficient. If Statement 1 is the only restriction, it is sufficient. If there could be other restrictions, the answer is E. There's no way to know, which is why you'll never see a question like this on the GMAT.

There isn't really any reason to learn how to solve a problem like this (using Statement 1). It's a kind of linear optimization problem that you learn how to solve in an MBA, but never need to solve on the GMAT. The numbers here are simple enough that you could work out the answer though - if you make 50 mohair blazers, you have 100 sewing hours 'left over' (you only use 100 of the 200 available). So we should use those hours to make the more profitable cashmere blazers, and since we need 4 extra sewing hours per cashmere blazer, we can make 25 of those instead of 25 mohair ones without exceeding either 200 hour limit.

mSKR · Answer

Cashmere: 10(4+6) hours gives profit 40$ = each hour profit= 4$
Mohair: 6 (4+2) hours gives profit 35$ = each hour profit: ~6$

A: 200 hours of cutting and 200 hours of sewing

Point1: Cutting and sewing can not be done separately
Point2: Sewing is determining factor; cutting time is same in both 
If I want to maximize profit, I should spend maximum hours on sewing of Mohair?

Option1:  Let me spend all hours on Mohair: 
200 hours/4= 50 cutting and need 100 hours on sewing .
100 hours left wasted.
Profit earned: 50*6=~300$

Option2:  Let me use maximum sewing time
Use cashmere : cutting 50
And sewing: 50*6= 300 hours.( extras)
Maximum usage: 200 hours of sewing: 200/6= I can only finish 33 cashmere suits
So profit in 200 hours: 33*6= 200$ only

Option1 and option2: gives me 100 extra hours in cashmere and 100 less hours in Mohair
Idea: let me balance 50%-50% to make it 200 hours usage of sewing time

In this case:
 Option3: 
25 cashmere+ 25 mohair
Total profit: 25*4+25*6= 100+ 150= 250$

So clearly , our winner is Option 1
 Hence sufficient

B. The wholesale price of cashmere cloth is twice that of mohair cloth.
Irrelevant information as profit is already mentioned in the question.

adroitpensador · Answer

Bunuel  request your help on this.

To me too, it felt tempting to not get to a unique solution and simply say "solution exists", mark (A) and move on. However, I spent that extra time to discover whether a unique solution exist or not. If we don't get a unique configuration of # of Mohair and # of Cashmere clothes, (A) statement won't be sufficient and answer in that case would be (E).

Is this thinking in the right direction? (wanting to optimize my time spent).

A certain clothing manufacturer makes only two types of men's blazer:

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