Please help! Special Applications Problem

A

audreyajyu

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Disclaimer: I am not looking for the direct answer, but am stuck on this assignment problem!
I understand a similar problem has been posted on the forum before, but I cannot understand the answers/comments given.

Here is my assignment:

KNIT'ting Industries also has innovative applications for the industry. One of their applications include developing color baths for knitting wools. The color baths are mixed using two different ingredients - the color and an agent that makes the color more UV stable. Other ingredients go into the color baths that are not important to the analysis. The mix of the two ingredients depends on the product type (knitting wool variety).

Consider two products SKU S06 (Product A) and R97 (Product B). You are asked to calculate the 'amount of blue color bath' for Product A and Product B. The following table indicates the amount of blue color (in liters) and UV agent (in liters) needed to prepare one litre of Product A and one litre of Product B.

Product AProduct B
Blue Color (in liters)0.1080.353
UV agent (in liters)0.4820.158

Suppose you have to prepare the blue color baths for Product A and Product B at the same time. You have 382 liters of blue color and 566 liters of UV agent available. How many liters of blue color bath for Product A and Product B can you prepare using the available inventory of the color blue and the UV agent?

--------------my work below----------------

I've attempted it in various ways but am stuck.

1) Blue color (L) = 0.108A + 0.353B
382=382(0.108)+382(0.353) =wrong answer

2) Solving by per product:
A= 0.108B+0.482UV =314.068 (amount of product A)
B=0.353B+0.158UV = 224.274 (amount of product B)
Got stuck here and don't know what to do next.

Q: how can I approach this problem, which kind of formula should I use?
Please lead me in the right direction, thank you all so much!
 
audreyajyu said:
Disclaimer: I am not looking for the direct answer, but am stuck on this assignment problem!
I understand a similar problem has been posted on the forum before, but I cannot understand the answers/comments given.

Here is my assignment:

KNIT'ting Industries also has innovative applications for the industry. One of their applications include developing color baths for knitting wools. The color baths are mixed using two different ingredients - the color and an agent that makes the color more UV stable. Other ingredients go into the color baths that are not important to the analysis. The mix of the two ingredients depends on the product type (knitting wool variety).

Consider two products SKU S06 (Product A) and R97 (Product B). You are asked to calculate the 'amount of blue color bath' for Product A and Product B. The following table indicates the amount of blue color (in liters) and UV agent (in liters) needed to prepare one litre of Product A and one litre of Product B.

Product AProduct B
Blue Color (in liters)0.1080.353
UV agent (in liters)0.4820.158

Suppose you have to prepare the blue color baths for Product A and Product B at the same time. You have 382 liters of blue color and 566 liters of UV agent available. How many liters of blue color bath for Product A and Product B can you prepare using the available inventory of the color blue and the UV agent?

--------------my work below----------------

I've attempted it in various ways but am stuck.

1) Blue color (L) = 0.108A + 0.353B
382=382(0.108)+382(0.353) =wrong answer

2) Solving by per product:
A= 0.108B+0.482UV =314.068 (amount of product A)
B=0.353B+0.158UV = 224.274 (amount of product B)
Got stuck here and don't know what to do next.

Q: how can I approach this problem, which kind of formula should I use?
Please lead me in the right direction, thank you all so much!
Click to expand...
I assume this is an assignment for a class you are attending.

You have two equations and two unknowns (B and UV).

Have you learned about solutions of simultaneous equation?
 
Dear Mr. Khan,

Taking your advice, I did the following calculations:
Assuming Product A & B is represented by x & y
Blue color = 382 L , UV = 566 L

0.108x +0.353y = 382
0.482x +0.158y = 566

For EQ1: y = (382-0.108x)/0.353

Substituting into EQ2: 0.482x + 0.158((382-0.108x)/0.353) = 566

I got x = 910.897227

Therefore, 0.353y=382-0.108x
If my x is correct, then y=283.623

Using these two values, I calculated:

Color bath for product A = 0.108(910.897227)+0.482(910.897227)=537.42936
Color bath for product Y= 0.353(283.623)+0.158(283.623) = 144.93135


But my answer is wrong, and I have only 3 attempt left on this question...
Please help!!


Thank you so much
 
So the total blue color will be EQUAL to 382 liters. and​

So the total UV color will be EQUAL to 566 liters.​

So if you make

A liters of product A and​
​
B liters of product B​

You would have

0.108 * A + 0.353 * B = 382 and ...................................(1)

0.482 * A + 0.158 * B = 566 ...........................................(2)

Solving those I get

A = 910.9 and B =803.5

Now you check answer by putting these values back into equations (1) and (2)
 
Thank you Mr. Khan, much appreciated!!
I see that I got the first part right when I got x = 910.897227

Thank you so much for your help!!
 
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