I will appreciate a hand in helping to solve this problem or give an hint on how to solve it, thanks

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oakes

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Cotton & Wool industries also have innovative applications for the industry. For example, they developed colors for knitting wools for special purpose applications. 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.
You are asked to calculate the amount of blue color bath you can prepare for Product A and Product B. You have 320 liters of blue color and 660 liters of UV agent. The following table indicates how much of the blue color (in liters) and how much of the UV agent (in liters) you need to make a liter of color bath for Product A and Product B.


Product A		Product B
Blue Color (in liters)0.2750.423
UV agent (in liters)0.6090.175
Suppose you have to prepare the color baths for Product A and Product B at the same time. How many liters of color bath for Product A and Product B can you prepare using the available inventory of the color blue and the UV agent?
(1) Amount of color bath for Product A
(2) Amount of color bath for Product B
 
You end up with a system of two inequalities. You can't make any more product than you have ingredients for.

in (1) we have

[MATH](0.275)N \leq 320\\ (0.609)N \leq 660[/MATH]
Solve that for the largest \(\displaystyle N\) you can.

Same with (2) but use the numbers for product B
 
So should we be solving for the system of two inequalities?
First one combining the constraints for Blue paint and the second combining the constraints for UV paint. My equations looks something like below,

0.275x+0.423y<=total of blue paint
0.609x+0.175y<= total of uv paint

I tried this way and couldn't reach the right answer, am I doing something wrong?
 
NanduV said:
So should we be solving for the system of two inequalities?
First one combining the constraints for Blue paint and the second combining the constraints for UV paint. My equations looks something like below,

0.275x+0.423y<=total of blue paint
0.609x+0.175y<= total of uv paint

I tried this way and couldn't reach the right answer, am I doing something wrong?
Click to expand...
Yes, possibly you are doing something wrong. If you share your work with us we might even be able to figure out what you are doing wrong. Does that make sense to you?
 
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