Special Applications: mixing blue dye, UV agent to make color baths: how many liters?

[zmalya]

Hello All,

I need some help with this.

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 S30 (Product A) and A46 (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 A	Product B
Blue Color (in liters)	0.26	0.536
UV agent (in liters)	0.647	0.283

Suppose you have to prepare the blue color baths for Product A and Product B at the same time. You have 315 liters of blue color and 674 liters of UV agent available. How many liters of Product A and Product B can you prepare using the available inventory of the color blue and the UV agent?

 

[BigBeachBanana]

Hello All,

I need some help with this.

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 S30 (Product A) and A46 (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 A	Product B
Blue Color (in liters)	0.26	0.536
UV agent (in liters)	0.647	0.283

Suppose you have to prepare the blue color baths for Product A and Product B at the same time. You have 315 liters of blue color and 674 liters of UV agent available. How many liters of Product A and Product B can you prepare using the available inventory of the color blue and the UV agent?

The problem seems to be missing the optimization objective.
1) Are you seeking to maximize the product of A and B, A over B, B over A, OR minimize the cost, etc...?
2) Is this a class exercise or a real-world problem?
3) What classes are you taking?
4) What's your math background?
5) Please share your attempts so we have a better understanding of your goals

 

[Steven G]

zmalya, please understand that this is a math help forum where helpers assist students with solving their problems. Keep in mind that if a helper were to simply give you the answer to your problem, then that wouldn't help you and the helper would be violating a forum policy.
If you had read the forum's posting guidelines you would have known how to make a proper post and would have been helped by now.