A manufacturing company plans to begin automating production and

Question

A manufacturing company plans to begin automating production and reducing its workforce by installing industrial robots at the start of each year over five years. Each robot will result in annual labor-cost savings of €150,000 beginning with the year of its installation and will have an upfront cost of €400,000. For robot installation in Year 1 of the program, the company will budget €600,000, plus the total amount of labor costs that will be saved by robotic production in that year. The robot-installation budget for each subsequent year will consist of the total amount of labor costs that will be saved by robotic production in that year plus any money left over from the previous year's robot-installation budget.

Statement: Within budget constraints, the maximum number of robots that can be installed in Year 1 of the program is ______X______, and the maximum number of robots that can be in service in Year 3 is _____Y_____.

Select values for X and for Y that create the statement that follows logically from the information provided. Make only two selections, one in each column.

Statement: Within budget constraints, the maximum number of robots that can be installed in Year 1 of the program is ______ X ______, and the maximum number of robots that can be in service in Year 3 is _____ Y _____.

Select values for  X  and for  Y  that create the statement that follows logically from the information provided. Make only two selections, one in each column.

ID: 700241

GMATGuruNY · Accepted Answer

Each time a robot is installed, we do the following:
REDUCE the budget by €400 (since each robot costs €400 to install)
INCREASE the budget by €150 (since each robot saves €150 in labor costs)
Implication:
Net cost for each installation = 400 spent - 150 saved = €250

1st year --> €600
Here, we can install 2 robots (at a net cost of €500), allowing us to apply the remaining €100 to next year's budget.

2nd year --> €100 carried over + €300 in labor savings for the 2 robots already installed = €400
Here, we can install 1 more robot (at a net cost of €250), allowing us to apply the remaining €150 to next year's budget.

3rd year --> €150 carried over + €450 in labor savings for the 3 robots already installed = €600
Here, we can install 2 more robots (at a net cost of €500), bringing the total number of robots to 5.

1st year --> 2 robots
3rd year --> 5 robots

egmat · Answer

This is one of those questions that even after watching the solution will keep you wondering – how is it possible to solve this question in about 2’15” (the alloted time for DI section). Well, let me tell you – to answer this question correctly, one will take longer than 2’15”. In fact, if one rushes through this question, they will most likely make a mistake since there are lots of opportunities to falter in this question.

So, first learning – if you are commiting to a question such as this one – commit fully – do not rush through it.

Now let’s get into all the points of failure in this question. It is quite a list – so I will focus only on the main ones.

First watch the solution.

https://www.youtube.com/watch?v=CFFybWUxRlw

Next observe the high level faltering points in this question.
 
 Not able to set up the left over budget expression
 
 Corrective action: Read the dataset with the intention of ‘owning the dataset’.   
 For the subsequent year, did not consider the robots made in the previous year for cost savings.
 
 Corrective action: Read the dataset with the intention of ‘owning the dataset’.   
 Not able to understand how to process the left over budget expression
 
 Corrective action: Draw inferences. Do not feel that if there are variables you cannot get any information.   
 Did not process beyond year 2 since you thought that this is too laborious, implying that you must have made a mistake somewhere.
 
 Corrective action: Understand that some DI questions will require more work. As long as you read the dataset with the mindset of ‘owning the dataset’, you will be good. Trust yourself!

chetan2u · Answer

Each robot will result in annual labor-cost savings of €150,000 beginning with the year of its installation and will have an upfront cost of €400,000.
 So, one time cost 400,000 and savings per year 150000. Additional cost of 250000 in the first year of installation

For robot installation in Year 1 of the program, the company will budget €600,000, plus the total amount of labor costs that will be saved by robotic production in that year.
 Amount available is 600000+150000x, where x is the number of robots installed that year.

The robot-installation budget for each subsequent year will consist of the total amount of labor costs that will be saved by robotic production in that year plus any money left over from the previous year's robot-installation budget.
 Amount available is 150000x+ any money left over, where x is the number of robots installed that year.

First year:  Let x be the number of robots installed. Cost incurred = 400000x and money available = 600000+150000x
Thus,  600000+150000x\geq 400000x......250000x\leq 600000.....x\leq 2.4 
So, 2 robots installed and 600000+150000*2-400000*2 or 100000 carried forward to next year

Second year:  Let y be the number of robots installed. Cost incurred = 400000y and money available = 100000+150000*(2+y)
Thus,  100000+150000(2+y)\geq 400000y......250000y\leq 400000.....y\leq 1.6 
So, 1 robot installed and 100000+150000(2+1)-400000*1 or 150000 carried forward to next year

Third year:  Let z be the number of robots installed. Cost incurred = 400000z and money available = 150000+150000*(2+1+z)
Thus,  150000+150000(3+z)\geq 400000z......250000z\leq 600000.....z\leq 2.4 
So, 2 robot installed

First year : 2
Third year : 2+1+2 or 5

Maxsparrow · Answer

Year 1
Budget + x (150 - 400)
600 - x (250)
Greatest X would be 2
Remaining Budget = 100

Year 2
Budget + saving from existing machine + a (-250)
100 + 300 - a (250)
greatest a would be 1
Remaining Budget = 150
Existing machine 3

Year 3
150 + 3(150) - b (250)
600 - b(250)
Greatest B would be 2

Hence:
x : 2
y : existing machine in Year 3 = 2 + 1 + 2 = 5

divyutdebbie · Answer

The trick to solving the question lies in the following sentence: The robot-installation budget for each subsequent year will consist of the total amount of labor costs that will be saved by robotic production in that year plus any money left over from the previous year's robot-installation budget.

KarishmaB · Answer

The thing to remember here is that as your fleet of robots increases, your saving per year increases.

Robot Cost = 400k
Saving per robot = 150k
So to buy a robot you need an additional 250k since a new robot will anyway bring its own saving of 150k along. Keep this 250k figure in mind.

First year  - Budget is 600k 
You have an additional 600k so you can buy 2 robots because you have an additional 2 * 250k. Then, 100k will be leftover for next year.
No of Robots in first year = 2 Robots

Second year  - 100k (leftover from last year) + 300K (savings from 2 existing robots) = 400k 
You can buy only 1 additional robot for 250k with the 400k. Then, 150k will be leftover for next year.
No of Robots in second year = 3 Robots

Third year  - 150k (leftover form last year) + 450k (savinsg from 3 existing robots) = 600k
You can buy 2 additional robots for 2*250k. Then, 100k will be leftover for next year.
No of Robots in third year = 5 Robots

ANSWER - 2, 5

user1937 · Answer

The worst thing one can do in such questions is get everything right, and miss the subtle point "robots in service" for blank 2. After a laborious and long solution, it is easy to rush and put in the second blank as robots produced and mark it as 2. Truly amazing question.

Gemmie · Answer

a: no. of robots installed in y1
b: no. of robots installed in y2
c: no. of robots installed in y3

year 1
600 + 150a >= 400a
=> 600 >= 250a
=> a <=2
=> X = 2

year 2
a = 2
=> leftover from y1: 600 + 150a - 400a = 600 - 2*250 = 100

100 + 150 * (b+2) >= 400b
=> 400 >= 250b
=> b = 1

year 3
a = 2; b = 1
=> leftover from y2: 100 + 150(a+b) - 400b = 100 + 150*4 - 400 = 150

150 + 150 * (c+3) >= 400c
=> 600 >= 250c
=> c <=2

Max a+b+c = 2 + 1 + 2 = 5
=> Y = 5

Aalto700 · Answer

I wonder how can you install  the 2nd robot  in the first yea, while you only get  saving 2  after you have completed installing the 2nd robot first.

The  order  of cash flow is 600 - 400 + 150  - 400   +150

Bunuel ,  KarishmaB

KarishmaB · Answer

Order of cashflow is irrelevant. The question doesn't give any cashflow constraint. It is given that the spending budget in the year includes the savings that will be realized that year. So the company is not waiting for the saving to accumulate. We have been given what the budgeting policy is. Any big company would have plenty of cashflows to make the purchases. The point is on what basis do you decide how many purchases to make every year.

Cost of the robot is 400k and saving from robot 150k so we just need 250k extra in the budget to buy a robot.

Cost of the robot is 400k and saving from robot 150k so we just need 250k extra in the budget to buy a robot.

Dragon805 · Answer

Hi  KarishmaB ,  Bunuel ,  Aalto700

Your answer is correct but however I think the order of cashflow is relevant too. Just that the order is 600k(budget) + 150k(savings from removing labor because they have planned for a robot) - 400k(actual cost of implementing the robot) (let me call this correct order) instead of what many people take it to be 600k - 400k + 150k. (let me call this wrong order). If we use the wrong order then clearly we can build only one robot in the first year with the given budget constraints but however if we use the correct order then we can build 2 robots in the first year. I dont think GMAT would want us to make the assumption of the company having more than the cash mentioned in the question.

Bunuel · Answer

Order does not affect the result. The Year 1 budget is defined as 600k  plus  the total savings generated in that same year from the robots installed.

So the available budget is 600k + 150kr (where r stands for the number of robots) while the required cost is 400k * r. We get 400kr <= 600k + 150kr, which simplifies to r <= 2.4, so at most 2 robots can be installed in Year 1.

Let's check: if r = 2: budget = 600k + 300k (savings from 2 robots) = 900k, cost = 800k, leaving 100k unused. No additional cash beyond what is specified is being assumed.

ChiranjeevSingh · Answer

Passage Analysis

A manufacturing company plans to begin automating production and reducing its workforce by installing industrial robots at the start of each year over five years.

We have a manufacturing company that plans to do two related things. One is automating production and the second is reducing the workforce. How will these two things be achieved? By installing robots at the start of each year over five years. So, at the beginning of each of the five years, the company will have some new industrial robots.

Each robot will result in annual labor-cost savings of €150,000 beginning with the year of its installation and will have an upfront cost of €400,000.

This statement gives us some numbers. One is that each robot will lead to a labor-cost saving of €150,000 and the saving will start in the year it is installed. So, we know that the robots are installed at the beginning of the year, so if you install a robot at the beginning of the current year, by the end of this year, you will have saved €150,000 in this year. And for each subsequent year, this robot will continue to save the same amount of labor cost. Each such robot has an upfront cost of €400,000.

For robot installation in Year 1 of the program, the company will budget €600,000, plus the total amount of labor costs that will be saved by robotic production in that year.

For the first year of the five-year period that we are talking about, the company has a budget of €600,000 plus the labor cost that will be saved by the robots in that year.

What does that mean? It means that if you are going to install two robots, the budget and cost would look like this:

Cost:  2 robots * €400,000/robot =  €800,000   
   Savings:  2 robots * €150,000/robot =  €300,000   
   Total Budget:  €600,000 (base) + €300,000 (savings) =  €900,000

The €800,000 cost is within the budget. However, it cannot install the third robot because the cost for three robots will be €1.2 million, whereas the budget will be €600,000 plus €450,000 of cost saving, so overall €1.05 million. So, the budget will be less than the upfront cost. The maximum for Year 1 is  2 robots .

A Note on the Process

At this point, it is important for me to share with you that this is the kind of analysis that will be going through my head as I read this question, even in the exam. Of course, since I am explaining here, I am a little more elaborate here, but at the same time, I want to tell you that I will be doing this kind of analysis: that if it installs two robots, then what's going to happen with the budget and the total cost? I assimilate deeply each and everything that comes to me and connect it to the previous context. Only then do I move on.

One of the critical and common flaws that I see in students is that they don't assimilate information. They just keep moving on. They understand a statement and then they just move on. They don't try to relate it and then assimilate what all it means so far. By the time they reach the end, a lot has gone on, and they have a very tentative hold on what has been said. It is a comprehension level problem: the process of comprehension is flawed. The process has to be about having a strong hold over what you have read so far. You don't continue reading with a very superficial understanding. You build a strong understanding and then you move on.

The robot-installation budget for each subsequent year will consist of the total amount of labor costs that will be saved by robotic production in that year plus any money left over from the previous year's robot-installation budget.

The statement talks about the robot installation budget for the subsequent years after year one. As we discussed, we can install only two robots in the first year, but by doing that, we have €100,000 left (€900,000 budget - €800,000 cost). For year two, the budget will be that €100,000 plus the labor cost savings. It is important to recognize that the labor cost savings will happen not just because of new robots installed in year two, but also from the robots installed in year one. Here is the breakdown for the Year 2 base budget:

Money Left Over from Year 1:  €900,000 (Y1 Budget) - €800,000 (Y1 Cost) =  €100,000   
   Savings from Existing Robots:  2 robots * €150,000/robot =  €300,000   
   Base Budget for Year 2:  €100,000 (leftover) + €300,000 (savings) =  €400,000

With that base budget, we can see if we can afford one new robot. Installing two new robots would have an upfront cost of €800,000, but would only lead to additional cost savings of €300,000, which is not enough. So, we can only install  1 new robot  in Year 2.

Question Analysis

Within budget constraints, the maximum number of robots that can be installed in Year 1 of the program is X, and the maximum number of robots that can be in service in Year 3 is Y.

The question being asked here is that within the budget constraints, the maximum number of robots that can be installed in year one of the program is two, as we have figured out, and the maximum number of robots that can be  in service  - this is a difference; it's not talking about the maximum numbers that can be installed in year three. It's talking about the number of robots in service; essentially, it's a summation of robots installed in year one + robots installed in year 2 + robots installed in year three.

At this stage, I will take a pause and I'll do the maths part to understand how many robots will be installed in year three.

Money Left Over from Year 2:  €550,000 (Y2 Budget) - €400,000 (Y2 Cost) =  €150,000   
   Robots in Service (start of Y3):  2 (from Y1) + 1 (from Y2) = 3 robots  
   Savings from Existing Robots:  3 robots * €150,000/robot =  €450,000   
   Base Budget for Year 3:  €150,000 (leftover) + €450,000 (savings) =  €600,000

This base budget of €600,000 is the same as Year 1's starting point, so we can install  2 new robots  in Year 3.

Given this understanding, we find the total number of robots in service in year three:

Year 1 Robots:  2  
   Year 2 Robots:  1  
   Year 3 Robots:  2  
   Total Robots in Service:  2 + 1 + 2 =  5 robots

A manufacturing company plans to begin automating production and

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