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The number of hours required for a certain company to produce
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01 Dec 2023, 09:32
01 Dec 2023, 09:32
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The number of hours required for a certain company to produce 1 unit of products X, Y, and Z, respectively, are shown in the table. Products X and Y can be produced simultaneously, and so can products X and Z; but products Y and Z cannot be produced simultaneously. What is the least number of hours required to produce a total of 10 units of product X, 5 units of product Y, and 7 units of product Z?
A. 35
B. 45
C. 55
D. 65
E. 85
Attachment:
2023-12-01_19-54-12.png [ 11.2 KiB | Viewed 5710 times ]
Attachment:
2023-12-01_19-55-24.png [ 74.91 KiB | Viewed 4151 times ]
Re: The number of hours required for a certain company to produce
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01 Dec 2023, 09:38
01 Dec 2023, 09:38
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guddo wrote:
The number of hours required for a certain company to produce 1 unit of products X, Y, and Z, respectively, are shown in the table. Products X and Y can be produced simultaneously, and so can products X and Z; but products Y and Z cannot be produced simultaneously. What is the least number of hours required to produce a total of 10 units of product X, 5 units of product Y, and 7 units of product Z?
A. 35
B. 45
C. 55
D. 65
E. 85
Attachment:
2023-12-01_19-54-12.png
Attachment:
2023-12-01_19-55-24.png
Since Y and Z cannot be produced simultaneously, let's calculate the amount of time required to produce 5 items of Y and 7 items of Z:
- 5 items of Y would require 5*4 = 20 hours.
- 7 items of Z would require 7*5 = 35 hours.
Since these products cannot be produced simultaneously, producing 5 items of Y and 7 items of Z together would require 20 + 35 = 55 hours.
Now, since producing 10 items of X requires 10*3 = 30 hours, and since item X can be paired either with products Y or Z, we can produce products X during those 55 hours without requiring additional time.
Therefore, only 55 hours are required to produce the required number of items.
Answer: C.
General Discussion
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Joined: 22 Dec 2016
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Re: The number of hours required for a certain company to produce
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01 Dec 2023, 23:07
01 Dec 2023, 23:07
guddo wrote:
The number of hours required for a certain company to produce 1 unit of products X, Y, and Z, respectively, are shown in the table. Products X and Y can be produced simultaneously, and so can products X and Z; but products Y and Z cannot be produced simultaneously. What is the least number of hours required to produce a total of 10 units of product X, 5 units of product Y, and 7 units of product Z?
A. 35
B. 45
C. 55
D. 65
E. 85
As we require the least number of hours, we need to ensure that the products are produced as simultaneously as possible.
We can divide the production into two groups -
- Group 1: X & Y ⇒ X & Y produces simultaneously
- Group 2: X & Z ⇒ X & Z produces simultaneously
For Group 1, in 12 hours, 4 units of X are produced and 3 units of Y are produced.
For Group 2, in 15 hours, 5 units of X are produced and 3 units of Z are produced.
Attachment:
Screenshot 2023-12-02 111515.png [ 37.38 KiB | Viewed 4930 times ]
Assume that the production of X and Y is simultaneous, hence, in 12 hours we will have 4 units of X and 3 units of Y. After 24 hours, we will have 8 units of X and 6 units of Y. We need only 5 units of Y, the production of X and Y can run simultaneously for 24 - 4 = 20 hours.
In 20 hours we have produced 6 units of X and 5 units of Y.
We still need 4 units of X and 7 units of Z. Now the production of X and Z can start. As fewer units of X is required and the production of X is faster than the production of Z, the time required will depend on the time to produce 7 units of Z.
Time required to produce 7 units of Z = 7 * 5 = 35 hours
Total time required = 35 + 20 = 55 hours
Hence, we can eliminate D and E as they are greater than 55. Option A cannot be true as well, as 7 * 5 = 35. This is possible when the production of X, Y, and Z occurs simultaneously.
Option B, 45, is not possible as well, because the production of 7 units of Z alone takes 35 hours. Hence, if we produce X and Z together and let the production run for 35 hours. We will still need at least 5 * 4 = 20 hours to produce Y alone. Hence, 55 is the least possible hours.
Option C
