Cotton & Wool industries also has innovative applications for the industry. For
ID: 391909 • Letter: C
Question
Cotton & Wool industries also has 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 327 liters of blue color and 632 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.
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?
Round your result to two decimal digit.
Amount of color bath for Product A:
Amount of color bath for Product B:
Produ Produ ct A ct B Blue Color 0.306 0.487 (in liters) UV agent (in liters) 0.627 0.447Explanation / Answer
Answer:
The calculation is as below with the help of linear equation in two variable technique.
0.306 X1 + 0.487 X2 = 327 …………..equ (1)
0.627 X1 + 0.447 X2 = 632 ………….equ (2)
From First equation, we can get
X1 = (327 – 0.487 X2 ) / 0.306 …………equ (3)
Put value of X1 from equ (3) in equa (2),
0.627 * (327 – 0.487 X2 ) / 0.306 + 0.447 X2 = 632
(0.627 * 327) / 0.306 –(0.627* 0.487 X2 ) / 0.306 + 0.447 X2 = 632
670.03 –0.998 X2 + 0.447 X2 = 632
670.03 –0.551 X2 = 632
–0.551 X2 = 632 -670.03
–0.551 X2 = - 38.03
X2 = 38.03 / 0.551
X2 = 69.02
From equ. (3), we can get the value of X1 as below by putting value of X2
X1 = (327 – 0.487 X2 ) / 0.306
X1 = (327 – 0.487 * 69.02 ) / 0.306
X1 = (327 –33.61 ) / 0.306
X1 = 293.39 / 0.306
X1 = 958.79
For making Product A, we need X1 amount of Blue and UV color and it will make total 894.55 liters for product A
For making Product B, we need X2 amount of Blue and UV color and it will make total 64.46 liters for product B
Product A Product B Product A Prodcut B Total (liters) X1 X2 958.79 69.02 Blue Color in Liter 0.306 0.487 327 293.39 33.61 UV Color in Liter 0.627 0.447 632 601.16 30.85 Total 894.55 64.46