An automated manufacturing plant uses robots to manufacture products. A generation-I robot working alone can manufacture a product in 30 hours whereas a generation-II robot working alone can manufacture the same product in 20 hours. If the manager of the plant wants the product manufacturing time to be greater than equal to 5 hours with at least 1 robot each of both generations working together, how many possible combinations of the number of robots of each generation is possible?a)4b)5c)6d)7e)8Correct answer is option 'E'. Can you explain this answer?

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An automated manufacturing plant uses robots to manufacture products. A generation-I robot working alone can manufacture a product in 30 hours whereas a generation-II robot working alone can manufacture the same product in 20 hours. If the manager of the plant wants the product manufacturing time to be greater than equal to 5 hours with at least 1 robot each of both generations working together, how many possible combinations of the number of robots of each generation is possible?

a)
4
b)
5
c)
6
d)
7
e)
8

Correct answer is option 'E'. Can you explain this answer?

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An automated manufacturing plant uses robots to manufacture products. ...

Given:

Generation-I Robot
- Time taken to manufacture a product = 30 hours
Generation-II Robot
- Time taken to manufacture the product = 20 hours
To Find: Possible combinations of number of generation-I and II robots such that the product manufacturing time ≥ 5 hours
Let the number of generation-I robots be x and number of generation-II robots be y

Approach:

We need to find the possible combination of the values of (x, y).
As we are given that the time taken for x generation-I and y generation-II robots should be greater than equal to 5 hours, we will formula an inequality in time taken for x generation robots and y generation-II robots to evaluate the possible combination of (x, y)
As Work = Rate * Time, for finding the time taken by the robots, we would need to find the work done and the rate
Number of products to be produced = 1
Now, we know that rate of production of n robots = n * rate of production of 1 robot.
So, once we find the rate of production of 1 robot for each generation, we can find the rate of production of x generation-I robots and y generation-II robots respectively.
As we are given the time taken by 1 generation-I robot and 1 generation-II robot to produce 1 product each, we can find the rate of production for robots of both generations.

Working out:

Generation-I
a. Work Done = 1 product
b. Time taken = 30 hours
c. Rate of manufacturing products = products per hour

Generation-II
a. Work Done = 1 product
b. Time taken = 20 hours
c. Rate of manufacturing products = 1/20 products per hour
3. Let’s assume there are x generation-I robots and y generation-II robots working together to produce 1 unit of product
a. So, work done = 1 product

b. Rate of x generation-I robots =

c. Rate of y generation-II robots =

4. As the time taken ≥ 5 hours, we can write

5. So, the possible combinations of {x, y} can be:
a. If y = 1, x = {1,2,3,4} – 4 options
b. If y = 2, x = {1,2,3} – 3 options
c. If x = 1, y = {1,2,3} – 3 options
d. However {x, y} = {1,1} and {1,2} is repeated.

6. So, we have a total of 10 -2 = 8 possible options
a. Please note that we have not considered x, y = 0 as we are given that at-least 1 robot of each generation should be working

Answer : E

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An automated manufacturing plant uses robots to manufacture products. A generation-I robot working alone can manufacture a product in 30 hours whereas a generation-II robot working alone can manufacture the same product in 20 hours. If the manager of the plant wants the product manufacturing time to be greater than equal to 5 hours with at least 1 robot each of both generations working together, how many possible combinations of the number of robots of each generation is possible?a)4b)5c)6d)7e)8Correct answer is option 'E'. Can you explain this answer? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about An automated manufacturing plant uses robots to manufacture products. A generation-I robot working alone can manufacture a product in 30 hours whereas a generation-II robot working alone can manufacture the same product in 20 hours. If the manager of the plant wants the product manufacturing time to be greater than equal to 5 hours with at least 1 robot each of both generations working together, how many possible combinations of the number of robots of each generation is possible?a)4b)5c)6d)7e)8Correct answer is option 'E'. Can you explain this answer? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An automated manufacturing plant uses robots to manufacture products. A generation-I robot working alone can manufacture a product in 30 hours whereas a generation-II robot working alone can manufacture the same product in 20 hours. If the manager of the plant wants the product manufacturing time to be greater than equal to 5 hours with at least 1 robot each of both generations working together, how many possible combinations of the number of robots of each generation is possible?a)4b)5c)6d)7e)8Correct answer is option 'E'. Can you explain this answer?.

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